2023高一上·全国·专题练习
1 . 在同一坐标系画出下列函数的图象. 通过观察两条曲线,说说它们的异同:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46fdb66640705da8c9c79eb38e3a4e.png)
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2 . 已知定义在
上的奇函数
,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/cd4440be-04d3-40a2-9c19-ebfe7b00c052.png?resizew=242)
(1)求函数
在
上的解析式;
(2)在坐标系中作出函数
的图象;
(3)若关于
的方程
恰好有三个不同的解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0b5d5192ac1e8ed68841d605e4c47d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/cd4440be-04d3-40a2-9c19-ebfe7b00c052.png?resizew=242)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)在坐标系中作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da3023b0765cfb1b268e29e1d01de0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-12-20更新
|
149次组卷
|
2卷引用:广东省汕头市潮阳区河溪中学2023-2024学年高一上学期第四学月考数学试题
名校
解题方法
3 . 已知函数
是定义在
的偶函数,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/010a4f28-c8d4-44e5-9c0c-e92d2b586353.png?resizew=215)
(1)请画出函数
图像,并求
的解析式;
(2)
,对
,用
表示
,
中的最大者,记为
,写出函数
的解析式(不需要写解答过程),并求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/c395237799431ccbd691c17d5c78ac3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/18/010a4f28-c8d4-44e5-9c0c-e92d2b586353.png?resizew=215)
(1)请画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f907172b5722b38303f01d833f90d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.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/316f701027f4bd38abca039b3499b498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
是定义在R的奇函数,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/f45c0d1a-cb19-4ff5-a946-235bca846105.png?resizew=243)
(1)请画出函数
图像并求
的解析式;
(2)
,对
,用
表示
,
中的最大者,记为
,写出函数
的解析式(不需要写解答过程),并求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119e06d01d35c30f2166624271535bff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/f45c0d1a-cb19-4ff5-a946-235bca846105.png?resizew=243)
(1)请画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74912a4bdbd89fb1d0b9fd10a1bc87b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a976d91358362fa49d6da8021fd47e2d.png)
![](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/316f701027f4bd38abca039b3499b498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c694cf892ee07daa54bdd9f2fb421e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c694cf892ee07daa54bdd9f2fb421e2.png)
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2023·全国·模拟预测
解题方法
5 . 已知函数
.
(1)在平面直角坐标系xOy中画出函数
的图象,并根据图象直接写出函数
的最大值;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/602ca768-5bb0-4a99-a537-cadbc5b1197d.png?resizew=183)
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6652da2b790105eed69ed335cf993955.png)
(1)在平面直角坐标系xOy中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/602ca768-5bb0-4a99-a537-cadbc5b1197d.png?resizew=183)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56024edbfd6c2097fb360471f128a753.png)
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6 . 设函数
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2617510d3739746b0633c37923fc9080.png)
(1)求实数
的值;
(2)判断函数的奇偶性,并说明理由;
(3)判断
在区间
上的单调性,并用函数单调性的定义证明结论;
(4)依据函数的性质,作出函数图象的示意图;
(5)若关于
的方程
恰有三个实数解,写出实数
的取值范围(不用证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd99584f8a2813059907e69d13581c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2617510d3739746b0633c37923fc9080.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)判断函数的奇偶性,并说明理由;
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e006fda65dd74bfed53c781c9b5f3a3.png)
(4)依据函数的性质,作出函数图象的示意图;
(5)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
7 . 设
是偶函数,且
时,
,求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/90e7b2d4-0346-459a-8963-9fceba1beeb7.png?resizew=148)
(1)
的解析式;
(2)画出
的图象,并由图直接写出它的单调区间和值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffa2b2fa52272ca3b60a319f6d632d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/90e7b2d4-0346-459a-8963-9fceba1beeb7.png?resizew=148)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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8 . 设函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/fbc49cbe-3e57-4dcc-99d4-58112f81b0a0.png?resizew=194)
(1)将函数
写成分段函数的形式,画出其图象;写出函数
的单调递减区间和值域;
(2)若
,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e59410318f0dc2e5530b27cd28ddf68.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/fbc49cbe-3e57-4dcc-99d4-58112f81b0a0.png?resizew=194)
(1)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdaffa9c15517afe6d7ba6488f88f67.png)
您最近一年使用:0次
名校
9 . 已知函数
.
(1)用分段函数的形式表示该函数并画出该函数的图象;
(2)写出此函数的单调区间(不需要写过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4475c74b364c8029b23679253e72a68a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/71aeafe0-a108-4522-9646-7ea5e746f219.png?resizew=185)
(1)用分段函数的形式表示该函数并画出该函数的图象;
(2)写出此函数的单调区间(不需要写过程).
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,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/7fbcf997-9b49-4250-ae7b-99d2a3a4f77c.png?resizew=171)
(1)求函数
的解析式,并画出
的图象;(作图要求先用铅笔作出图象,再用黑色签字笔将图象描黑);
(2)根据图象写出函数
的单调区间(不用证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/bd8ed92f58d44ee590c425bc741195c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/7fbcf997-9b49-4250-ae7b-99d2a3a4f77c.png?resizew=171)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据图象写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次