【题文】以下命题正确的是
【题文】以下命题正确的是
题型:难度:来源:
【题文】以下命题正确的是
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033654-45934.png)
;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033654-39712.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033654-60999.png)
必要非充分条件;
(3)函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033655-36087.png)
;
(4)若奇函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033655-96352.png)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033655-75088.png)
,则函数图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033656-88639.png)
对称.
答案
【答案】(1)(2).
解析
【解析】
试题分析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033656-25442.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033656-36219.png)
,故正确;
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033656-42903.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033657-19588.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033657-96184.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033654-60999.png)
必要非充分条件,故正确;
(3)令
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033657-66114.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033658-68741.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033658-79236.png)
上为减函数,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033658-36231.png)
;
(4)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033659-79242.png)
为奇函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033659-34013.png)
,又因为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033655-75088.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033659-31985.png)
,即函数图像关于
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033700-88445.png)
对称.
考点:函数的性质.
举一反三
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033627-92864.png)
,则下列说法正确的是( )
①
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033628-57512.png)
关于点
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033628-68571.png)
成中心对称
②
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033628-57512.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033628-67149.png)
单调递增
③当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033629-68925.png)
取遍
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033629-11378.png)
中所有数时不可能存在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033629-65171.png)
使得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033630-88840.png)
【题文】给出下列命题;
①设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033529-42325.png)
表示不超过
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033529-74590.png)
的最大整数,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033529-60505.png)
;
②定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033530-27515.png)
上的函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033530-16172.png)
,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033530-19618.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033531-99761.png)
的图象关于
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033531-59860.png)
轴对称;
③函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033531-78443.png)
的对称中心为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033531-11137.png)
;
④已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033531-77265.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033532-12579.png)
处有极值
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033532-78591.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033532-19755.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033533-80620.png)
;
⑤定义:若任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033533-22038.png)
,总有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033541-80780.png)
,就称集合
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033541-55581.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033542-21247.png)
的“闭集”,已知
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033542-15382.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033541-55581.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033542-40234.png)
的“闭集”,则这样的集合
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033541-55581.png)
共有7个。
其中正确的命题序号是____________.
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033518-40249.png)
的图象的对称中心是(3,-1),则实数
.
【题文】给出下列命题;
①设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033449-15873.png)
表示不超过
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033450-67372.png)
的最大整数,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033450-59901.png)
;
②定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033451-14427.png)
上的函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033451-49603.png)
,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033451-94319.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033452-13969.png)
的图象关于
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033452-31116.png)
轴对称;
③函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033452-61074.png)
的对称中心为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033452-83256.png)
;
④已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033453-29607.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033453-92589.png)
处有极值
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033453-66694.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033454-34511.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033454-47243.png)
;
⑤定义:若任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033454-59116.png)
,总有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033455-37080.png)
,就称集合
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033455-63217.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033455-67435.png)
的“闭集”,已知
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033456-55449.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033455-63217.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033456-58184.png)
的“闭集”,则这样的集合
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327033455-63217.png)
共有7个。
其中正确的命题序号是____________.
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