解题方法
1 . 函数的性质通常指函数的定义域、值域、单调性、奇偶性、零点等.已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b768fd17982b07fc369d72e1049807.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/5d557983-b0d7-4fc0-a63d-8f37b8e47c68.png?resizew=216)
(1)研究并证明函数
的性质;
(2)根据函数
的性质,画出函数
的大致图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b768fd17982b07fc369d72e1049807.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/5d557983-b0d7-4fc0-a63d-8f37b8e47c68.png?resizew=216)
(1)研究并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)根据函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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解题方法
2 . 给定函数
,
,
,
,用
表示
,
,
中的较小者,记为
.
![](https://img.xkw.com/dksih/QBM/2023/11/30/3379051373395968/3379334206119936/STEM/1bf1704c28554918b744f605ef91b9c4.png?resizew=273)
(1)求函数
的解析式,画出其图象,根据图象写出函数的单调区间;
(2)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7343e8f9118952329c5c1072caa9b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcecc8ac651ab4c23a34eaf5c8b2c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2108f1d868fd218dc2a26d1749d64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7183e25f3c656714ab09aa80641f960b.png)
![](https://img.xkw.com/dksih/QBM/2023/11/30/3379051373395968/3379334206119936/STEM/1bf1704c28554918b744f605ef91b9c4.png?resizew=273)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd84da85388fcc2b7b74eed6790b9318.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e1cb9d08ff6f810c1172d917d2f56a.png)
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解题方法
3 . 已知定义在
上的奇函数
满足:当
时,
,当
时,
.
(1)在平面直角坐标系中画出函数
在
上的图象,并写出单调递减区间;
(2)求出
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21c6260bcade05f3a432841f449b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab25c22afca1cbed90677c7f629809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b6fd5a1dbb65cbe9bfe602c914a24f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(1)在平面直角坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/21/27c2790f-0269-4266-8e07-4dbb06c26c88.png?resizew=229)
(2)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-11-21更新
|
83次组卷
|
2卷引用:广东省汕头市潮南区阳光实验学校2023-2024学年高一上学期第三次月考数学试题
名校
4 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/fa258bee-7ce0-4613-8f74-fde8a408fb58.png?resizew=216)
(1)画出
的图象;
(2)根据图象写出函数的单调区间;
(3)求
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a560d0c6969b117a5a8f88f87a8380.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/fa258bee-7ce0-4613-8f74-fde8a408fb58.png?resizew=216)
(1)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)根据图象写出函数的单调区间;
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bf0995f32a13d0a9e423f3e88ab271.png)
您最近一年使用:0次
名校
5 . 函数
(1)画出函数的图象;
(2)当
时,写出
的单调区间,并求函数在区间上的值域(直接写值域,不要过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da3a7e0520cb1c89967304c7a406f0.png)
(1)画出函数的图象;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd04947978c9ef82e651a52f848c653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/28/d6cb0811-d69c-4392-9086-74498ea59feb.png?resizew=224)
您最近一年使用:0次
名校
解题方法
6 . 函数
,
(1)解关于
的不等式
;
(2)若
,
①若
,求证
;
②画出
的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5ee992e4d7904e80e246a908fe9051.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e342b2932a0414a3221e961c0e116aa.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764f981a79d9850e2fd2afb79940da50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e297f6897dec36236986df208904d9.png)
②画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
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解题方法
7 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5e2f76311de78baf7c42c3a9c955ae.png)
(1)将函数写成分段函数并画出函数的图像;
(2)求
的值;
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5e2f76311de78baf7c42c3a9c955ae.png)
(1)将函数写成分段函数并画出函数的图像;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1e8ae93be5d4f44440dc3d2613d0ea.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6ad4d23e3a0c6bf7a538e577081b7e.png)
您最近一年使用:0次
解题方法
8 . 已知函数
是定义在
上的奇函数,且当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/dcf14905-2467-48bc-894a-4cc7a8492abb.png?resizew=205)
(1)求函数
的解析式并画出其图象;
(2)求函数
的单调区间;
(3)设函数
在
上的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7b4162be068735915bfb30b315632c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/dcf14905-2467-48bc-894a-4cc7a8492abb.png?resizew=205)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba87f4580bdba2a3e71dcc347df1479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7028a2a582526386c5ea7babcebf073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7028a2a582526386c5ea7babcebf073.png)
您最近一年使用:0次
名校
9 . 已知函数
是定义域为
的奇函数,且
时,
.
(1)求
的解析式;
(2)在给定坐标系中画出函数
的图象,并讨论方程
(
为常数)根的个数(写出结果即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf51d9719b5dba6b64411e961002d3a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)在给定坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c604e08a0837f160207b05dec72decaf.png)
(1)求
;
(2)若
,求
的取值范围
(3)画出
的图象,并写出函数的单调区间和值域. (直接写出结果即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c604e08a0837f160207b05dec72decaf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/04f311e6-4902-47de-9306-93206a178ea0.png?resizew=179)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe561b2dcc4f0f68fbca0b8cf4cecc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8739b1c13e4375e746a1f7856abfe7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次