题目内容
给出下列四个命题:
①函数
与函数
表示同一个函数;
②奇函数的图象一定通过直角坐标系的原点;
③函数
的图像可由
的图像向上平移1个单位得到;
④若函数
的定义域为
,则函数
的定义域为
;
⑤设函数
是在区间
上图象连续的函数,且
,则方程
在区间
上至少有一实根;
其中正确命题的序号是 .(填上所有正确命题的序号)
①函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928468437.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928483604.png)
②奇函数的图象一定通过直角坐标系的原点;
③函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928499581.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928515531.png)
④若函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928530447.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928546415.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928561523.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928561390.png)
⑤设函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928593491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928608435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928624778.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928639569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928608435.png)
其中正确命题的序号是 .(填上所有正确命题的序号)
③⑤
试题分析:①因为函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928468437.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928483604.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928702597.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928468437.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928483604.png)
②奇函数的图像一定通过直角坐标系的原点,此命题错误,若奇函数在x=0处没定义,则奇函数的图像就不过原点;
③函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928499581.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928515531.png)
④因为函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928530447.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928546415.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928795715.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928561523.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928827359.png)
⑤设函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928593491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928608435.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928624778.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928639569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928608435.png)
点评:此题考查的知识点较多,较为综合,属于中档题。抽象函数的有关问题对同学们来说具有一定的难度,特别是求函数的定义域,很多同学解答起来总感棘手,鉴于此,我们在学习时要善于总结。①已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928593491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928936610.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928593491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928967502.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928936610.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928998696.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928936610.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928936610.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928593491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928936610.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928967502.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928967502.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001929123491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824001928593491.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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