题目内容
已知一次函数y1=kx+b的图象分别过点A(-1,1),B(2,2).(1)在直角坐标系中直接画出函数y2=|x|的图象;
(2)根据图象写出方程组
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_ST/0.png)
(3)根据图象回答:当x为何值时,y1<y2.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_ST/images1.png)
【答案】分析:(1)函数y2=|x|的图象即是y=x与y=-x且y>0的部分图象;
(2)观察图象可知是y1与y2的交点坐标;
(3)观察图象可知分为两部分,一部分为-x>kx+b,一部分为x>kx+b.
解答:解:(1)如图所示:
(2)∵A(-1,1),B(2,2).
∴
,![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/images1.png)
∴
,
∴一次函数y1=kx+b为:y1=
x+
,
联立
与
,
即可得:
,
;
∴方程组
的解为:
,
;
(3)当x>2或x<-1时,y1<y2.
点评:此题考查了一次函数的知识,培养学生的观察能力.注意待定系数法与数形结合思想的应用.
(2)观察图象可知是y1与y2的交点坐标;
(3)观察图象可知分为两部分,一部分为-x>kx+b,一部分为x>kx+b.
解答:解:(1)如图所示:
(2)∵A(-1,1),B(2,2).
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/images1.png)
∴
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/1.png)
∴一次函数y1=kx+b为:y1=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/3.png)
联立
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/5.png)
即可得:
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/6.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/7.png)
∴方程组
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/9.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022154917404794521/SYS201310221549174047945021_DA/10.png)
(3)当x>2或x<-1时,y1<y2.
点评:此题考查了一次函数的知识,培养学生的观察能力.注意待定系数法与数形结合思想的应用.
![](http://thumb2018.1010pic.com/images/loading.gif)
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