下表中,y是x的一次函数.x2125y631215(1)求该函数的表达式,并补全表格;(2)已知该函数图象上一点M(1,-3)也在反比例函数图象上,求这两个函数图象的另一交点N的坐标.
2023-04-27
问题描述:
麻烦大家看看这个题下表中,y是x的一次函数.x | ![]() | 1 | 2 | 5 | |
y | 6 | ![]() | ![]() | ![]() |
(1)求该函数的表达式,并补全表格;
(2)已知该函数图象上一点M(1,-3)也在反比例函数
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007505498.png)
最佳答案:
(1)y=-3x,补全表格见解析;(2)(-1,3).
试题分析:(1)设y=kx+b,将任已知两点代入可得函数解析式,从而补全表格.
(2)将点M的坐标代入,可得m的值,联立一次函数及反比例函数解析式可得另一交点坐标.
试题解析:解:(1)设该一次函数为y=kx+b(k≠0),
∵当x=-2时,y=6,当x=1时,y=-3,
∴,解得:
.
∴一次函数的表达式为:y=-3x.
∵当x=2时,y=-6;当y=-12时,x=4,
补全表格如下:
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007458170.png)
1
2
4
5
6
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007458170.png)
-6
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007458170.png)
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007458170.png)
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007505498.png)
∴
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007661448.png)
∴反比例函数解析式为
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007677507.png)
联立可得
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007692756.png)
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007708633.png)
![](https://img1.runjiapp.com/duoteimg/tiku/imgs/http://pic2.mofangge.com/upload/papers//20140823/20140823034007724633.png)
∴另一交点坐标为(-1,3).
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