1 . 某同学用“五点法”画函数
在某一个周期内的图象时,列表并填入了部分数据,如下表:
(1)请在答题卷上将上表
处的数据补充完整,并直接写出函数
的解析式;
(2)设
,求函数
的值域;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e221ad8f28f138eac3d428051da7ace7.png)
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | 1 | ![]() | ![]() | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec4b4a628ce4482e16a3edc2953fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c3a3d28b1cb09b6c49102a21d7534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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2 . (1)在用“五点法”作出函数
的大致图象的过程中,第一步需要将五个关键点列表,请完成下表:
(2)设实数
且
,求证:
;(可以使用公式:
)
(3)证明:等式
对任意实数
恒成立的充要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467a953b54798b6e2dcd6d76f8817938.png)
0 | |||||
0 | |||||
1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d95727eed094e7ceb6663ee9d39bda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141ba74bc522b95958aea59cdc8c93d0.png)
(3)证明:等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83576aaf57c7ebdcf56110fdbb0c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d8ae1706a9ea5df3eca17eaa5c8b71.png)
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3 . 已知函数
的最小正周期为
,且当
时,函数有最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/46b31fcf-f6ef-459e-9578-9fa709e13302.png?resizew=252)
(1)求
的解析式;
(2)作出
在
范围内的大致图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002806220e70a9661a58ef8c848604aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24db7b603aebdee8e298d1fe49c848e1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/46b31fcf-f6ef-459e-9578-9fa709e13302.png?resizew=252)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260bb3786192dfcca715e41a3e0b6f44.png)
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