【题文】已知函数,,有下列4个命题:①若,则的图象关于直线对称;②与的图象关于直线对称;③若为偶函数,且,则的图象关于直线对称;④若为奇函数,且,则的图象关于直
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044641-61322.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044641-84715.png)
,有下列4个命题:
①若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044641-42264.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-11772.png)
对称;
②
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-72395.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-25984.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-83850.png)
对称;
③若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
为偶函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044643-50664.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-83850.png)
对称;
④若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
为奇函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044643-30517.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-11772.png)
对称.
其中正确的命题为_
__ ____ .
答案
【答案】 ①②③④
解析
【解析】
试题分析:①中令
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044643-87136.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044643-79213.png)
化为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044643-92436.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044643-23049.png)
对称;②中
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044644-79371.png)
关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044644-84150.png)
对称的函数解析式就是将原式中的
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044644-92853.png)
换成
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044644-81078.png)
就行了,即是
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044644-12201.png)
所以②正确;③中
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
为偶函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044645-98457.png)
用
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044645-42939.png)
换
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044644-92853.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044645-81058.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
的图象关于直线x=2对称是对的;④中,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044645-56121.png)
,说明函数图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044645-53771.png)
对称。
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044642-51698.png)
为奇函数,它的图象关于原点对称,所以函数图象也关于直线x=1对称,④正确.
考点:函数的对称性,函数的奇偶性.
举一反三
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044632-13225.png)
是定义在R上的周期为3的周期函数,如图表示该函数在区间(-2,1]上的图像,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044633-30274.png)
+
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044633-13246.png)
=( )
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044633-67617.jpg)
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044555-69275.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044556-42066.png)
,有下列4个命题:
①若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044556-34606.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-21722.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-82845.png)
对称;
②
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-45942.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-95168.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044558-32027.png)
对称;
③若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-21722.png)
为偶函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044558-37802.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-21722.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044558-32027.png)
对称;
④若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-21722.png)
为奇函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044558-83197.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-21722.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044557-82845.png)
对称.
其中正确的命题为_
__ ____ .
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044542-27323.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044542-87951.png)
上的奇函数,若对于任意的实数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044542-86767.png)
,都有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044542-67252.png)
,且当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044542-43787.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044543-89453.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044543-62377.png)
的值为 ( )
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044522-47027.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044522-56785.png)
上的奇函数,若对于任意的实数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044522-30511.png)
,都有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044523-24985.png)
,且当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044523-47886.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044523-20138.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327044524-32396.png)
的值为 ( )
最新试题
热门考点