名校
1 . 仔细阅读下面三个函数性质:
(
)对任意实数
,存在常数
,使得
.
(
)对任意实数
,存在常数
,使得
.
(
)对任意实数
,存在常数,使得
.
请写出能同时满足以上三个性质的函数(不能为常函数)的解析式__________ .(写出一个即可)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c171d0021b15415b055c223935a2292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156d0e8f3176584a06f774a7a15c99ac.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357f35cfcdc9cc8f655290cebaa90bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a1c02c533c60949a994212c90fbeda.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a0ad869e385be373c7037214397b9e.png)
请写出能同时满足以上三个性质的函数(不能为常函数)的解析式
您最近一年使用:0次
名校
2 . 高斯是德国著名数学家,近代数学奠基者之一,享有“数学王子”称号,他和阿基米德、牛顿并列为世界三大数学家,用其名字命名的“高斯函数”为:设
,用
表示不超过x的最大整数,则
称为高斯函数,例如
,
.已知函数
,函数
,则下列4个命题中
①函数
不是周期函数;②函数
的值域是
;
③函数
的图象关于
对称; ④方程
只有一个实数根;
其中全部正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b7f26fe1977bda9de200debe99f020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810007b04c5d4a231d9b1063cb170116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289ba8096d112966e08fa50b6bbc613d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfc47c74df6e203349793c7009f04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4d549992fdd4a1a57b46e56d4e1875.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cb03b1d99872b6fe877e1ee5141418.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e688d3ca6190b722b4b0858120e0bd3.png)
其中全部正确结论的序号是
您最近一年使用:0次