1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c8eae7bf6251fd35cbcfce082f9dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)当
时,若
,求x的值:
(2)若
是偶函数,求出m的值:
(3)
时,讨论方程
根的个数.并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c8eae7bf6251fd35cbcfce082f9dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ce70cd93ab5e129a18d4df247063fc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54078c4af5b305e26b8e3faa6423e67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
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解题方法
2 . 已知函数
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/3d1bd810-67ab-46d9-93e0-a0afa9a3e87b.png?resizew=210)
(1)判断函数
的奇偶性并用定义证明;
(2)用分段函数的形式表示函数
的解析式,并直接在本题给出的坐标系中画出函数
的图像;
(3)用
表示
,
中的较大者,即
,若
,则求
的值 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578b5d562457a6ba731ee5a2dd3b1fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63716f1f42c412f23bfb2f3651638c4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/3d1bd810-67ab-46d9-93e0-a0afa9a3e87b.png?resizew=210)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)用分段函数的形式表示函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c694cf892ee07daa54bdd9f2fb421e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b345ba4baeae1041f7d69ad09dc326c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe57503d720d07a26770942b067d2cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 对于每个实数x,若函数
取三个函数
的最小值,则函数
的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29e777f335399c71bd6ee7b3c1df6fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() | B.![]() | C.![]() | D.4 |
您最近一年使用:0次
解题方法
4 . 为进一步改善空气质量,增强人民的蓝天幸福感,
年
月
日,国务院公开发布
打贏蓝天保卫战三年行动计划
,其中京津冀地区被列为重点治理区域.某课外活动小组根据北京市预报的某天
时
空气质量指数数据绘制成散点图,并选择连续函数
来近似刻画空气质量指数
随时间
变化的规律
如图
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/964fa465-1aac-449b-ae8d-8c0b06626075.png?resizew=306)
(1)求
,
的值;
(2)当空气质量指数大于
时,有关部门建议市民外出活动应戴防雾霾口罩,并禁止某行业施工作业.请你结合该课外活动小组选择的函数模型,回答以下问题:
(i)某同学该天
:
出发上学,是否应该戴防雾霾口罩?请说明理由;
(ii)试问该天
:
之后,该行业可以施工作业的时间最长为多少小时?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6567511bb9486b2ca7452b870abd2a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b0e787c1d82071c825975348698f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461950348087cdb06ec28d7569d14c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf4ba80c2b40227655676eb6b34d461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861b1123fa7fc6df45d115cb3cbc0b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/964fa465-1aac-449b-ae8d-8c0b06626075.png?resizew=306)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)当空气质量指数大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7afc6e67a875ed2eb889e950a77715.png)
(i)某同学该天
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8937d7f5eb113bdd1d4eb407d9bfad.png)
(ii)试问该天
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8937d7f5eb113bdd1d4eb407d9bfad.png)
您最近一年使用:0次
解题方法
5 . 已知函数
的图像经过点
.
(1)求函数
的解析式;
(2)判断函数
在
上的单调性并证明;
(3)当
时,
的最小值为3,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0df848bc19edcbe6daf56f36a8b56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8be8de0230f64e618c6a7362f3099d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae61f4eb1e4f52cb48e523d0065bd49.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387e9eb75d1b04eee0c50b3a38f90c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
为
上的奇函数,当
时,
.
(1)求
的值;
(2)求
的解析式.
(3)写出解不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be315e528951120e7d551f654d2a1f5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)写出解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7a75bcd70f6b1a6d02dbb92e964e1b.png)
您最近一年使用:0次
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解题方法
7 . 若不等式
对于
恒成立,则实数
的取值范围是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6192abce444df59b1f83e94bc916ad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
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解题方法
8 . 已知函数
,满足
.
(1)求
值;
(2)在
上,函数
的图象总在一次函数
的图象的上方,试确定实数m的取值范围;
(3)设当
时,函数
的最小值为
,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592744129d3499498fee320ae874645e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b3e4e9e74fb4ce9b3d96cd4a504035.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f9bd7fdb0c44b5e2e1d5a59dd6f7dd.png)
(3)设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972f9920cd64e5abb65c57b799afe09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3466b71d1d9117438ed50388a57d9397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82a1224e47f31ecdfffd328d5a3ab6d.png)
您最近一年使用:0次
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9 . 已知函数
.
(1)用定义证明
是奇函数;
(2)判断函数
在
上的单调性,并用单调性定义进行证明;
(3)若
,求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28f8ca25a8e35bf38783813cce5cda4.png)
(1)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66ef59c3970f3581a5ea29e21fd564d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
10 . 已知函数
是
上的增函数,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad02c301ea9623462d229958a33a0623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-07更新
|
857次组卷
|
2卷引用:北京市东直门中学2023-2024学年高一上学期期中考试数学试卷