1 . 已知幂函数
的图象过点
,设函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/cd4263a7-d085-4bf6-94e2-f246dc892b0d.png?resizew=183)
(1)求函数
的解析式、定义域,判断此函数的奇偶性;
(2)根据“定义”研究函数
的单调性,画出
的大致图象(简图),并求其值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e5abce9e520b37572b68141940bbf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687c95902f2c7a5cb9808ace73b7bbad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/cd4263a7-d085-4bf6-94e2-f246dc892b0d.png?resizew=183)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据“定义”研究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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解题方法
2 . 已知函数
是定义在
上的奇函数,且
.
(1)求a,b值;
(2)用定义证明:
在
上单调递减;
(3)解关于t的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212cc812d22ec59949f7f9d553d1220d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8814adea623063b3042db129841da313.png)
(1)求a,b值;
(2)用定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
(3)解关于t的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06da5f9311195b66c3e8d1ecb90df3f.png)
您最近一年使用:0次
2023-12-22更新
|
216次组卷
|
2卷引用:山东省临沂市2023-2024学年高一上学期期中考试数学试题
3 . 已知函数
为定义域内的奇函数,且
时,
,
(1)求
时,
的解析式
(2)利用函数单调性定义,求函数
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977bf639a9dc22b6fdca878e55f050e6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)利用函数单调性定义,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7760261a04d65e7e16cc124e106dec2.png)
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解题方法
4 . 已知函数
的定义域是
,若对于任意
,都有
,且
时,有
.
(1)令
,求
的定义域
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b9676b221e3f25206444afeb77c698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa901949b8294aa95d3bec25b990543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450868427afd4832db685d1d3516c0fc.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
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5 . 已知函数
对于任意的
,都有
成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
A.![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
6 . 已知函数
,证明:
在区间
上单调递增的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f67ebe3b975f0b846a38a76eff0dbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2952239f733e7978b2abb3c20fafcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aacce9a2647b42f0c4cc10020950573.png)
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解题方法
7 . 已知函数
满足:
,
.令
.
(1)求
值,并证明
为偶函数;
(2)当
时,
.
(i)判断
在
上的单调性,并说明理由;
(ii)若
,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2671f593186fa00f17ad26eba7b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db13144a4b27bc76c6ca989423fe95e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6e28dbfcdd6fb66b9ff759be044287.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
(i)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a669b4be098e4e54f5b06d92835f55c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9c7bcef11dcd9a207c7eed2e6eb884.png)
您最近一年使用:0次
名校
解题方法
8 . 设函数
,
是定义域为
的奇函数.
(1)确定
的值.
(2)若
,判断并证明
的单调性;
(3)若
,使得
对一切
恒成立,求出
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2889dcd7359e699493cac47bda278fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3687573b9a457376b00af451efb02b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7d2bb9fd6de312a742ef10c81b9b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
9 . 已知函数
(
),其中
.
(1)若
,求函数
的最小值;
(2)若
,讨论并证明函数
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0d18a0a39f1dc23e382f5fc762635b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d0b969f58a09dff5c32b43219e2080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
10 . 已知
.
(1)求
的解析式;
(2)试判断函数
在
上的单调性,并用单调性的定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2ef5d32fb1000535fc95878d7e9a26.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1b322a7e2dbe40f17a0f9c61ec4aa.png)
您最近一年使用:0次