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【330167】19.2.3 一次函数与方程、不等式

时间:2025-02-08 16:50:58 作者: 字数:3467字

19.2.3 一次函数与方程、不等式


一.选择题(共8小题)

1.一次函数y=kx+b的图象如图所示,则方程kx+b=0的解为(  )

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

Ax=2 By=2 Cx=﹣1 Dy=﹣1


2.一次函数y=kx+bkb为常数,且k≠0)的图象如图所示,根据图象信息可求得关于x的方程kx+b=0的解为(  )

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

Ax=﹣1 Bx=2 Cx=0 Dx=3

3.一元一次方程ax﹣b=0的解x=3,函数y=ax﹣b的图象与x轴的交点坐标为(  )

A.(30 B.(﹣30 C.(a0 D.(﹣b0

4.已知方程kx+b=0的解是x=3,则函数y=kx+b的图象可能是(  )

A <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> B <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> C <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> D <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

5.若方程x﹣3=0的解也是直线y=4k+1x﹣15x轴的交点的横坐标,则k的值为(  )

A.﹣1 B0 C1 D±1

6.如图,直线y1=x+by2=kx﹣1相交于点P,点P的横坐标为﹣1,则关于x的不等式x+bkx﹣1的解集在数轴上表示正确的是(  )

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

A <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> B <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> C <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> D <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

7.如图,直线y=﹣x+my=nx+4nn≠0)的交点的横坐标为﹣2,则关于x的不等式﹣x+mnx+4n0的整数解为(  )

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

A.﹣1 B.﹣5 C.﹣4 D.﹣3

8.如图,一次函数y=kx+b的图象经过AB两点,则不等式kx+b0的解集是(  )

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

Ax0 B0x1 Cx1 Dx1

二.填空题(共10小题)

9.若直线y=2x+bx轴交于点(﹣30),则方程2x+b=0的解是 _________ 

10.如图是一次函数y=kx+b的图象,则方程kx+b=0的解为 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

11.一次函数y=kx+bkb为常数,且k≠0)的图象如图所示,根据图象信息可求得关于x的方程kx+b=0的解为 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

12.如图,已知直线y=ax﹣b,则关于x的方程ax﹣1=b的解x= _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>


13.如图,直线y=kx+b分别交x轴和y轴于点AB,则关于x的方程kx+b=0的解为 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

14.如图,已知函数y=2x+by=ax﹣3的图象交于点P(﹣2,﹣5),根据图象可得方程2x+b=ax﹣3的解是 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

15.如图,已知函数y=2x+b与函数y=kx﹣3的图象交于点P,则不等式kx﹣32x+b的解集是 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

16.如图,直线y=kx+bA(﹣12)、B(﹣20)两点,则0≤kx+b≤﹣2x的解集为 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

17.一次函数y1=kx+by2=x+a的图象如图,则kx+bx+a的解集是 _________ 


 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

18.如图,函数y=kx <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的图象相交于A a2),则不等式 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a> 的解集为 _________ 

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

三.解答题(共4小题)

19.如图,根据函数y=kx+bkb是常数,且k≠0)的图象,求:

1)方程kx+b=0的解;

2)式子k+b的值;

3)方程kx+b=﹣3的解.

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>

20.如图,直线l1y=2x与直线l2y=kx+3在同一平面直角坐标系内交于点P

1)写出不等式2xkx+3的解集: _________ 

2)设直线l2x轴交于点A,求△OAP的面积.

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>


21.在平面直角坐标系x0y中,直线y=kx+bk≠0)过(13)和(31)两点,且与x轴、y轴分别交于AB两点,求不等式kx+b≤0的解.

 <a href="/tags/165/" title="等式" class="c1" target="_blank">等式</a> <a href="/tags/380/" title="方程" class="c1" target="_blank">方程</a> <a href="/tags/844/" title="不等式" class="c1" target="_blank">不等式</a> <a href="/tags/885/" title="函数" class="c1" target="_blank">函数</a>



22.在直角坐标系xOy中,直线y=kx+bk≠0)经过(﹣21)和(23)两点,且与x轴、y轴分别交于AB两点,求不等式kx+b≥0的解集.