题目内容
甲同学家到乙同学家的途中有一公园,甲从家到公园的距离与乙从家到公园的距离都是2 km,甲10时出发前往乙家.如图所示,表示甲从家出发到达乙家为止经过的路程y(km)与时间x(分)的关系.试写出y=f(x)的函数解析式.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525196697021.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525196697021.png)
f(x)=![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525196851837.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525196851837.png)
解:当x∈[0,30],设y=k1x+b1,
由已知得![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052519700938.png)
∴k1=,b1=0,y=
x;
当x∈(30,40)时,y=2;
当x∈[40,60]时,设y=k2x+b2,
由已知得![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525197321089.png)
∴k2=
,b2=-2,y=
x-2.
∴f(x)=![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525196851837.png)
由已知得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052519700938.png)
∴k1=,b1=0,y=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052519716335.png)
当x∈(30,40)时,y=2;
当x∈[40,60]时,设y=k2x+b2,
由已知得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525197321089.png)
∴k2=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052519747333.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052519747333.png)
∴f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240525196851837.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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