1 . 设函数
,且
.
(1)求
的解析式;
(2)写出函数
具有的性质(至少两个,不用证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf658d1d64a6e30197d236bbbb2667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4caa14fbdb776f997a74f866962519a2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/2018/10/29/2064216064172032/2069093490728960/STEM/db59573d-0d0a-408c-8b41-615fc20af164.png)
(1)证明:
是偶函数;
(2)在给出的直角坐标系中画出
的图象;
(3)求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3b46ec6a5c699609421b8e8491c59b.png)
![](https://img.xkw.com/dksih/QBM/2018/10/29/2064216064172032/2069093490728960/STEM/db59573d-0d0a-408c-8b41-615fc20af164.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)在给出的直角坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2018-11-05更新
|
398次组卷
|
2卷引用:四川省眉山一中办学共同体2018-2019学年高一上学期半期考试数学试卷
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7be673c414a75d47bd9f3a873b1e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7be673c414a75d47bd9f3a873b1e8f.png)
(1)求f(-4)、f(5)的值;
(2)画出函数f(x)的图象,并指出它的单调区间(不需证明);
(3)当时,求函数的值域.
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4 . 对于定义域分别是A,B的函数
,
,规定:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9c39db44d84f43fc9722bb979fc095.png)
现给定函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ced635c8a3f61072d7b9532efc7283d.png)
(1) 若
,写出函数
的解析式;
(2) 当
时,求问题(1)中函数
的值域;
(3) 请设计一个函数
,使得函数
为偶函数且不是常数函数,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b9c39db44d84f43fc9722bb979fc095.png)
现给定函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ced635c8a3f61072d7b9532efc7283d.png)
(1) 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311ae2bedaa43832f1d025294c48e97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2) 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966d9dd819cba29980da3700422c2497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(3) 请设计一个函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
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解答题-问答题
|
适中(0.65)
|
5 . (2011年苏州20)已知二次函数
对于任意的实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
,
都有
成立,且
为偶函数.
(1)证明:实数
>0;
(2)求实数a与b之间的关系;
(3)定义区间
的长度为
,问是否存在常数
,使得函数
在区间
的值域为
,且
的长度为
?若存在,求出a的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811986d3ad64d6919ee64b1367577b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f3560f0c5eedffa5ce38fde2db28c3.png)
都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c337371338c0661b46fa8d0467fdfa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25990e1d373ac30d7480633e47cc1ef.png)
(1)证明:实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求实数a与b之间的关系;
(3)定义区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d796cc708c99b7415397b8c93b1cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72131c00caddb160678989ce9c0f4b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5b21aa3df433d6b78b76b36e21adcc.png)
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