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【324221】2024八年级数学下册 专题6.2 反比例函数的图象与性质重难点题型(含解析)(新版)

时间:2025-01-15 21:43:49 作者: 字数:19396字
简介:


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 专题6.2反比例函数的图象与性质-重难点题型

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

Shape1 知识点1 反比例函数的图象与性质】

1、图象:由两条曲线组成(双曲线)

2、性质:

函数

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

图象

所在象限

增减性

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

  1. 三象限

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

在同一象限内, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的增大而减小

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

  1. 四象限

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

在同一象限内, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的增大而增大

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 越大,函数图象越远离坐标原点

【题型1反比例函数的图象】

【例1】(南江县期末)函数y=﹣kx+k和函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 在同一坐标系内的图象可能是(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】分两种情况讨论,当k0时,分析出一次函数和反比例函数所过象限;再分析出k0时,一次函数和反比例函数所过象限,符合题意者即为正确答案.

【解答】解:①当k0时,y=﹣kx+k过一、二、四象限;y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 过一、三象限;

k0时,y=﹣kx+k过一、三、四象象限;y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 过二、四象限.

观察图形可知只有A符合.

故选:A

【变式1-1】(河北模拟)直线yax+b与双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象如图所示,则ab+c的结果(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

A.大于0 B.小于0 C.等于0 D.无法确定

【分析】根据一次函数和反比例函数图象和系数的关系即可求得a0b0c0

【解答】解:∵直线yax+b经过一、三、四象限,

a0b0

双曲线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象在一、三象限,

c0

ab+c0

故选:A

【变式1-2】(金平区校级期末)如图是三个反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x轴上方的图象,由此观察得到k1k2k3的大小关系为 k1k2k3 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】本题考查反比例函数与的图象特点.

【解答】解:读图可知:三个反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象在第二象限;故k10y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 在第一象限;且y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象距原点较远,故有:k1k2k3;综合可得:k1k2k3.故填k1k2k3

【变式1-3】(伊川县期末)函数ykx+by <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> kb≠0)在同一坐标系中的图象可能是图中的(  )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】根据一次函数的图象与系数的关系,由一次函数ykx+b图象分析可得kb的符号,进而可得kb的符号,从而判断y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> kb≠0)的图象是否正确,进而比较可得答案.

【解答】解:A、函数ykx+b的图象经过第一、二、四象限,则k0b0,则kb0,所以函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> kb≠0)的图象经过第二、四象限,故A选项不符合题意;

B、函数ykx+b的图象经过第二、三、四象限,则k0b0,则kb0,所以函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> kb≠0)的图象经过第一、三象限,故B选项不符合题意;

C、函数ykx+b的图象经过第一、二、三象限,则k0b0,则kb0,所以函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> kb≠0)的图象经过第一、三象限,故C选项不符合题意;

D、函数ykx+b的图象经过第二、三、四象限,则k0b0,则kb0,所以函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> kb≠0)的图象经过第一、三象限,故D选项符合题意;

故选:D

【题型2反比例函数的性质】

【例2】(淮北月考)对于反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,下列结论:①图象分布在第二、四象限;②当x0时,yx的增大而增大;③图象经过点(1,﹣2);④若点Ax1y1),Bx2y2)都在图象上,且x1x2,则y1y2,其中正确的是(  )

A.①②③ B.②③④ C.①③④ D.①②④

【分析】根据题目中的函数解析式和反比例函数的性质,可以判断各个小题中的结论是否正确.

【解答】解:∵于反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

该函数的图象分布在第二、四象限,故①正确;

x0时,yx的增大而增大,故②正确;

x1时,y=﹣2,故③正确;

若点Ax1y1),Bx2y2)都在图象上,且x1x2,则点A和点B都在第二象限或都在第四象限时y1y2,点A在第二象限,点B在第四象限时y1y2,故④错误;

故选:A

【变式2-1】(新泰市月考)已知函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 是反比例函数,且图象位于第一、三象限,则n 2 

【分析】由反比例函数的定义及反比例函数图象位于第一、三象限,即可得出关于n的一元二次方程及一元一次不等式,解之即可得出n的值.

【解答】解:∵函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 是反比例函数,且图象位于第一、三象限,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

n2

故答案为:2

【变式2-2】(诸城市三模)反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象在二、四象限,则一次函数yax+a的图象所在象限是(  )

A.一、二、三 B.一、三、四 C.一、二、四 D.二、三、四

【分析】先根据反比例函数的增减性判断出a的符号,再根据一次函数的图象与系数的关系判断出次函数yax+a的图象经过的象限即可.

【解答】解:∵反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象在二、四象限,

1﹣a0

a1

一次函数yax+a的图象经过一、二、三象限,

故选:A

【变式2-3】(清涧县期末)已知函数y1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,当2≤x≤3时,函数y1的最大值是a,函数y2的最小值是a﹣4,求ak的值.

【分析】由反比例函数的性质可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> a <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> a﹣4,可求a的值和k的值.

【解答】解:∵y1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2≤x≤3

y1的值随x值的增大而减小,y2的值随x值的增大而增大.

x2时,y1的最大值为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> a

x2时,y2的最小值为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> a﹣4

∴﹣aa﹣4

解得a2

Shape2 k4

【知识点2 反比例函数图象的对称性】

1)中心对称,对称中心是坐标原点

2)轴对称:对称轴为直线Shape3 和直线Shape4

【题型3反比例函数图象的对称性】

【例3】(滨海县一模)如图,已知直线ymx与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的一个交点坐标为(34),则它们的另一个交点坐标是 (﹣3,﹣4) 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】反比例函数的图象是中心对称图形,则与经过原点的直线的两个交点一定关于原点对称.

【解答】解:因为直线ymx过原点,双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的两个分支关于原点对称,

所以其交点坐标关于原点对称,一个交点坐标为(34),另一个交点的坐标为(﹣3,﹣4).

故答案是:(﹣3,﹣4).

【变式3-1】(沂源县期末)若图中反比例函数的表达式均为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,则阴影面积为4的有(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

A1 B2 C3 D4

【分析】根据反比例函数比例系数k的几何意义,反比例函数的性质以及三角形的面积公式,分别求出四个图形中阴影部分的面积,即可求解.

【解答】解:图1中,阴影面积为4

2中,阴影面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 42

3中,阴影面积为2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 44

4中,阴影面积为4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 48

则阴影面积为4的有2个.

故选:B

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【变式3-2】(兰州期末)如图,在直角坐标系中,正方形的中心在原点O,且正方形的一组对边与x轴平行,点P4aa)是反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k0)的图象上与正方形的一个交点,若图中阴影部分的面积等于16,则k的值为(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

A16 B1 C4 D.﹣16

【分析】根据反比例函数的中心对称性得到正方形OABC的面积=16,则4a×4a16,解得a1a=﹣1舍去),所以P点坐标为(41),然后把P点坐标代入y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 即可求出k

【解答】解:∵图中阴影部分的面积等于16

正方形OABC的面积=16

P点坐标为(4aa),

4a×4a16

a1a=﹣1舍去),

P点坐标为(41),

P41)代入y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,得

k4×14

故选:C

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【变式3-3】(茶陵县模拟)如图,点P3aa)是反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k0)与⊙O的一个交点,图中阴影部分的面积为10π,则反比例函数的解析式为 y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】根据圆的对称性以及反比例函数的对称性可得,阴影部分的面积等于圆的面积的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,即可求得圆的半径,再根据P在反比例函数的图象上,以及在圆上,即可求得k的值.

【解答】解:设圆的半径是r,根据圆的对称性以及反比例函数的对称性可得:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> πr210π

解得:r2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

P3aa)是反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k0)与⊙O的一个交点.

3a2k

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> r

a2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 24

k3×412

则反比例函数的解析式是:y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

故答案是:y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

Shape5 知识点3 反比例函数比例系数Shape6 的几何意义

如图,在反比例函数Shape7 上任取一点Shape8 ,过这一点分别作Shape9 轴,Shape10

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 垂线Shape11 Shape12  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 坐标轴围成的矩形Shape13 的面积Shape14






【题型4反比例函数中k的几何意义】

【例4(莫旗二模)如图,直线lx轴于点P,且与反比例函数y1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)及y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)的图象分别交于点AB,连接OAOB,已知△OAB的面积为3,则k1k2 6 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】由反比例函数的图象过第一象限可得出k10k20,再由反比例函数系数k的几何意义即可得出SOAP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k1SOBP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2,根据△OAB的面积为2结合三角形之间的关系即可得出结论.

【解答】解:∵反比例函数y1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)及y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)的图象均在第一象限内,

k10k20

APx轴,

SOAP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k1SOBP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2

SOABSOAPSOBP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k1k2)=3

解得:k1k26

故答案为:6

【变式4-1】(梓潼县模拟)如图,矩形ABCD的顶点A和对称中心在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k≠0x0)的图象上,若矩形ABCD的面积为10,则k的值为(  )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

A10 B4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> C3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> D5

【分析】设A点的坐标为( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> )则根据矩形的性质得出矩形中心的坐标为:( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),即( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),进而可得出BC的长度.然后将坐标代入函数解析式即可求出k的值.

【解答】设A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),

AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

矩形的面积为10

BC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

矩形对称中心的坐标为:( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),即( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

对称中心在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象上,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

mk﹣5m0

mk﹣5)=0

m0(不符合题意,舍去)或k5

故选:D

【变式4-2】(巴中)如图,平行于y轴的直线与函数y1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)和y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)的图象分别交于AB两点,OA交双曲线y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 于点C,连接CD,若△OCD的面积为2,则k 8 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】解一:设Am <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),则Bm <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),Dm0),设Cn <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),由SOCD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ODyc <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2,得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> .又SOCDSOADSACD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2,即可求出k8

解二:过点CCEx轴于E,根据反比例函数比例系数k的几何意义得出△OCE的面积为1,由△OCD的面积为2,得出点EOD的中点.再证明点COA的中点,那么SOAD2SOCD4,进而求出k8

【解答】解一:设Am <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),则Bm <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),Dm0),设Cn <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),

SOCD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ODyc <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

SOCDSOADSACD

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> mn

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2

k8

解二:如图,过点CCEx轴于E

C在双曲线y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 上,

SOCE1

SOCD2

SECDSOCE1

EOD的中点,

CEAD

COA的中点,

SOAD2SOCD4

函数y1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)的图象过点AADx轴,

k8

故答案为:8

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【变式4-3】(深圳模拟)如图,在平面直角坐标系xOy中,矩形OABC的两边OCOA分别在x轴、y轴的正半轴上,反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)分别与边AB、边BC相交于点E、点F,且点E、点F分别为ABBC边的中点,连接EF.若△BEF的面积为3,则k的值是 12 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】设B点的坐标为(ab),根据中点求得EF的坐标,再把EF坐标代入反比例函数解析式,得kab的关系式,再根据△BEF的面积为3,列出ab的方程,求得ab,便可求得k

【解答】解:∵四边形OCBA是矩形,

ABOCOABC

B点的坐标为(ab),

E、点F分别为ABBC边的中点,

E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> b),Fa <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> b),

EF在反比例函数的图象上,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k

SBEF3

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 3,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 3

ab24

k <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ab12

故答案为:12

【题型5反比例函数图象上点的坐标特征】

【例5】(上城区一模)已知直线y=(a﹣2bx与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 相交于点( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,﹣2),那么它们的另一个交点坐标是 ( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2) 

【分析】由直线y=(a﹣2bx与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 相交于点( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,﹣2),即可得出函数解析式,再求另一个交点坐标.

【解答】解:方法一:∵直线y=(a﹣2bx与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,相交于点( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,﹣2),

a﹣2b <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 3xy3b+a <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

直线为y=﹣3x

双曲线为y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

解方程组: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

另一个交点为( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2).

故答案为:( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2).

方法二:∵直线y=(a﹣2bx是正比例函数,

直线y=(a﹣2bx与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的交点关于原点对称,

直线y=(a﹣2bx与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 相交于点( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,﹣2),

它们的另一个交点坐标为:( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2).

故答案为:( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 2).

【变式5-1(自贡模拟)若点A(﹣1y1),B2y2),C3y3)在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象上,则y1y2y3的大小关系是(  )

Ay1y2y3 By1y3y2 Cy2y3y1 Dy3y2y1

【分析】先根据函数解析式中的比例系数k确定函数图象所在的象限,再根据各象限内点的坐标特点及函数的增减性解答.

【解答】解:∵在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 中,k=﹣(a2+1)<0

此函数图象在二、四象限,

∵﹣10

A(﹣1y1)在第二象限,

y10

320

B2y2),C3y3)两点在第四象限,

y20y30

32

y2y30

y1y2y3的大小关系为y1y3y2

故选:B

【变式5-2】(雁塔区校级模拟)若点A在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 上,点A关于y轴的对称点B在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 上,则k1+k2的值为 0 

【分析】设A点坐标为(ab),由点在反比例函数图象上点的特征可求得k1abk2=﹣ab,进而可求解.

【解答】解:设A点坐标为(ab),

A在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 上,

k1ab

A关于y轴的对称点B在反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 上,

B(﹣ab),

k2=﹣ab

k1+k2ab+(﹣ab)=0

故答案为0

【变式5-3】(浙江模拟)如图,在平面直角坐标系中,ABAC5,点B和点C的坐标分别为(﹣20),(40),反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)的图象经过点A,且与AC相交于另一点D,作AEBC于点E,交BD于点F,则点F的坐标为 (1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ) 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】由ABACAEBC得到AE的长度和点A的坐标,再求出k的大小和直线AC的解析式,再求出点D的坐标,从而得到直线BD的解析式,最后再求出点F的坐标.

【解答】解:∵点B和点C的坐标分别为(﹣20),(40),

BC6OB2

ABAC5AEx轴,

BECE3

OEBEOB1AE4

A14),

k1×44

反比例函数的解析式为y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

设直线AC的解析式为ykx+b,则

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

直线AC的解析式为y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

D的坐标为(3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ),

设直线BD的解析式为ymx+n,则

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

直线BD的解析式为y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

x1时,y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

F的坐标为(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ).

故答案为:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ).

【题型6反比例函数与一次函数的交点问题】

【例6】(新吴区期末)已知正比例函数y1k1xk1≠0)与反比例函数y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2≠0)的图象有一个交点的坐标为(3,﹣1),则关于x的不等式k1x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 0的解集为 x<﹣30x3 

【分析】利用反比例函数和正比例函数的性质判断两个交点关于原点对称,然后根据关于原点对称的点的坐标特征写出另一个交点的坐标.根据交点坐标和图象即可得出不等式的解集.

【解答】解:∵正比例函数y1k1xk1≠0)与反比例函数y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2≠0)的图象关于原点对称,

正比例函数y1k1xk1≠0)与反比例函数y2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k2≠0)的图象的交点关于原点对称,

一个交点的坐标为(3,﹣1),

另一个交点的坐标是(﹣31),如图,

则关于x的不等式k1x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 0的解集为x<﹣30x3

故答案为:x<﹣30x3

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【变式6-1】(安徽模拟)如图,直线yax+ba≠0)与双曲线y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> k≠0)交于点Am,﹣1.5)和点B(﹣23),则不等式ax+b <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的解集是 x≤﹣20x≤4 

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】由点AB都在反比例函数图象上可得﹣1.5m=﹣2×3,从而求出m,然后根据图象交点求解.

【解答】解:∵点AB都在反比例函数图象上,

∴﹣1.5m=﹣2×3

m4

x≤﹣20x≤4ax+b <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

故答案为:x≤﹣20x≤4

【变式6-2】(阿坝州)如图,一次函数ykx+b与反比例函数y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)的图象交于Am6),Bn3)两点.

1)求一次函数的解析式;

2)求△AOB的面积.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】(1)首先求出AB两点坐标,再利用待定系数法即可解决问题;

2)求得直线与x轴的交点,然后根据SAOBSAOCSBOC求得即可.

【解答】解:(1)把Am6),Bn3)两点坐标代入y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x0)可得m2n4

A26),B43),

一次函数ykx+b的图象经过点AB

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

一次函数的解析式为y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x+9

2)设直线与x轴的交点为C

y0代入y <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x+9,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x+90,解得x6

C60),

SAOBSAOCSBOC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 9

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【变式6-3】(凉州区校级二模)如图,一次函数的图象ykx+b与反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象在第一象限交于点A43),与y轴的负半轴交于点B,且OAOB

1)求一次函数ykx+b与反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的表达式;

2)请直接写出不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的解集.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

【分析】(1)由点A的坐标利用反比例函数图象上点的坐标特征即可求出a值,从而得出反比例函数解析式;由勾股定理得出OA的长度从而得出点B的坐标,由点AB的坐标利用待定系数法即可求出直线AB的解析式;

2)观察第一象限双曲线在直线下方的部分自变量的范围即可.

【解答】解:(1)∵点A43)在反比例函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象上,

k4×312

反比例函数解析式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> OAOB,点By轴负半轴上,

B0,﹣5).

把点A43)、B0,﹣5)代入ykx+b中,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

一次函数的解析式为y2x﹣5

2)令y2x﹣5y0,则x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> ,∴D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 0),

由图象可知,不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的解集为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> x4

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/264/" title="难点" class="c1" target="_blank">难点</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/411/" title="反比例" class="c1" target="_blank">反比例</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>


1