题目内容
(本题满分12分)
一次函数
与指数型函数
,(
)的图像交于两点
,解答下列各题
:
(1)求一次函数
和指数型函数
的表达式;
(2)作出这两个函数的图像;
(3)填空:当
时,
;当
时,
。
一次函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537042678.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537058665.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537074506.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537105745.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240035371201299.png)
(1)求一次函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537136447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537152442.png)
(2)作出这两个函数的图像;
(3)填空:当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537167332.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537167595.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537167332.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537198627.png)
(1)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240035372302497.png)
(3)
,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537276786.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537214815.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240035372302497.png)
(3)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537245366.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537276786.png)
试题分析:(1)因为两个函数的图像交于两点
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537105745.png)
所以有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537292848.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537308799.png)
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537323474.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537339519.png)
所以两个函数的表达式为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537214815.png)
(2)如图所示,为所画函数图像
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240035372302497.png)
(看图像给分)…………………………9分
(3)填空:当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537167332.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537245366.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537167595.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537167332.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537276786.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824003537198627.png)
点评:已知函数类型求解析式,待定系数法是常用的方法,通过本题说明要体会函数图象的应用,利用图像得到函数性质
![](http://thumb2018.1010pic.com/images/loading.gif)
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