题目内容
已知偶函数f(x)(x∈R),当
时,f(x)= -x(2+x),当
时,f(x)=(x-2)(a-x)(
).关于偶函数f(x)的图象G和直线
:y=m(
)的3个命题如下:
当a=2,m=0时,直线
与图象G恰有3个公共点;
当a=3,m=
时,直线
与图象G恰有6个公共点;
,使得直线
与图象G交于4个点,且相邻点之间的距离相等.其中正确命题的序号是(A)
A. ①② B. ①③ C. ②③ D. ①②③
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819645544.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819661626.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819676457.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819723486.png)
当a=2,m=0时,直线
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
当a=3,m=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819754303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240158198011001.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
A. ①② B. ①③ C. ②③ D. ①②③
A
试题分析:根据题意,由于偶函数f(x)(x∈R),当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819645544.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819661626.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819676457.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819661626.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819941242.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819723486.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819754303.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240158198011001.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824015819692280.png)
点评:主要是考查了函数性质的运用,属于中档题。
![](http://thumb2018.1010pic.com/images/loading.gif)
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