名校
1 . 设
,函数
.
(1)若
,求证:函数
为奇函数;
(2)若
,判断并证明函数
的单调性;
(3)若
,函数
在区间
上的取值范围是
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6fe56c70ed96e7f0ee48063dae9fc7.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/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e6fca71fccb890f3ad8501ea4f560e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d42f621464019a86fadf05723784e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2023-03-14更新
|
644次组卷
|
3卷引用:福建省漳州市第三中学2022-2023学年高一上学期期中数学试题
名校
2 . 已知二次函数
的值域为
.
(1)判断此函数在
上的单调性,并用单调性的定义证明你的结论;
(2)求出
在
上的最小值
,并求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6942f56d4009e67ac0f8be67d6009fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(1)判断此函数在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457087d04fc36a2e218d5bf5723f335d.png)
(2)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)用函数单调性的定义证明:
在
上是增函数;
(2)求函数
在区间
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b42ec94a554c8faacadd7c14ff7bc9.png)
(1)用函数单调性的定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334919736e5ed881f691e4ca738b4ce.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dccf1f9faac56117d6d3dd1dddd286d.png)
您最近一年使用:0次
2023-11-02更新
|
1149次组卷
|
5卷引用:福建省泉州市泉州科技中学2023-2024学年高一上学期期中数学试题
福建省泉州市泉州科技中学2023-2024学年高一上学期期中数学试题北京市交通大学附属中学2023-2024学年高一上学期期中考试数学试题北京市海淀区北京交通大学附属中学2023-2024学年高一上学期期中练习数学试题(已下线)第三章 函数的概念与性质【单元基础卷】-【满分全攻略】(人教A版2019必修第一册)(已下线)专题01 函数的单调性证明考点(期末大题1)-期末题型秒杀技巧及专项练习(人教A版2019必修第一册)
名校
解题方法
4 . 已知函数
.
(1)
在区间
上的单调性并利用定义证明:
(2)求
在区间
上的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3cac51dd02874e8c19c2e081d1d80f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530e48690edc3429da2d23c25151296.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530e48690edc3429da2d23c25151296.png)
您最近一年使用:0次
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee88e8e3af2021c4eeb829ae182ad2e.png)
(1)用定义证明
是偶函数;
(2)用定义证明
在
上是减函数;
(3)作出函数
的图象,并写出函数
当
时的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee88e8e3af2021c4eeb829ae182ad2e.png)
(1)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96977a5415357a1b31b00b91b511f884.png)
(3)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
,且
.
(1)求
的值,并证明:
在区间
上单调递减;
(2)若
对
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ec94edfff2dc57f83635e6b8d8913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6266a5b47e313651b98ca48c91a754fc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62273885d6ef20061be80cd13882c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce2837a8732f5038a0245b69306d20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
解题方法
7 . 已知函数
是奇函数
.
(1)求
的值;
(2)判断
在区间
上的单调性,并证明;
(3)当
时,若对于
上的每一个
的值,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1a4fa622dcfa9d561ea48fdf085a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b93abe2a497b7ef3cb8c1b9de8492e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c624c9ae14ea1ce323ce33d7f2cde0.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f88173ef0c29bedd0155b7893d2474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90bfd0944c7ad6082f12f363231b256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2023-10-13更新
|
548次组卷
|
3卷引用:福建省建瓯市芝华中学2023-2024学年高一上学期期中考试数学试题
名校
解题方法
8 . 已知函数
,
.
(1)判断并用定义证明
在
上的单调性;
(2)若
在
上的最大值为m,且
(
,
),求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cac46fe7735b2b1f998cbfb4372b871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(1)判断并用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)若
![](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/ab04de6651256f6281e9f4c1dc3c7955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd311f055e0ab607145b36b915cd116e.png)
您最近一年使用:0次
解题方法
9 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/9c7ba11b-6e71-472f-9ac1-bbd5e551049f.png?resizew=192)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/f7f692f8-7409-4b4c-85d5-15070c5a70e2.png?resizew=192)
(1)在同一坐标系中画出函数
,
的图象;
(2)定义:对
,
表示
与
中的较小者,记为
,分别用函数图象法和解析法表示函数
,并写出
的单调区间和值域(不需要证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945106a06b33e0107ce9c8b30ddb0a74.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/9c7ba11b-6e71-472f-9ac1-bbd5e551049f.png?resizew=192)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/f7f692f8-7409-4b4c-85d5-15070c5a70e2.png?resizew=192)
(1)在同一坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)定义:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f832d9cca2d5c9d76d38374e2a258d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4febc53921a6ed12d250651c3dacd61b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
您最近一年使用:0次
解题方法
10 . 已知函数
是定义在
上的奇函数,且
.
(1)求a,b的值,并用定义证明:函数
在区间
上的单调性;
(2)若
,求实数a的取值范围;
(3)写出函数
的值域(不必写出解答过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4456fb2e3fd38c13353aa0d894ec43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3213a7a72b5e376ee25efd535398fb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd60e05922c00cf442c5099a3d73959.png)
(1)求a,b的值,并用定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3213a7a72b5e376ee25efd535398fb7d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e9dba36c87a25407342e262f9f9c30.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
您最近一年使用:0次