名校
1 . 已知函数①
;②
,作出函数
的图象,并写出单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b33d559cb7cd4d3c45ab237179de345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e980c3a147bdccef4f5165bad2d41c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-03-13更新
|
123次组卷
|
2卷引用:北京市第五十中学分校2023-2024学年高一上学期期中练习试卷
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)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
.
(1)当
时,画出函数图象并指出函数
的最大值和最小值;
(2)求实数
的取值范围,使
在区间
上是单调函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389df5bf66ae866f474083813c20bbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944c02f1425e9c700c928b5a542bd04b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71dbce0ccda0f5df7d0555fa23bf770.png)
您最近一年使用:0次
解题方法
4 . 已知函数
.
(1)画出函数
的图象,并写出函数
的值域及单调区间;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/b8511c19-24a7-4003-850f-eeaa5809bd99.png?resizew=163)
(2)解不等式
;
(3)若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32648060f5e3e810c65f962fa2ea41b0.png)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/b8511c19-24a7-4003-850f-eeaa5809bd99.png?resizew=163)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476e65208aaf36809ee0d65fc61c4dbb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a743e9d797611bdc5fea0621668bb78c.png)
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名校
5 . 已知函数
.
(1)求
和
;
(2)若
,求
的值;
(3)作出函数
的图象;并根据图象写出单调区间;
(4)当方程
有3个解时,直接写出实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2e92fcc7b2d36880047071a0f95e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14348dcf52b54174c7f3cecc63d69e3e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(4)当方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
您最近一年使用:0次
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
名校
7 . 已知函数
.
(1)判断函数
的奇偶性并证明;
(2)用定义证明函数
在
上单调递增;
(3)画出函数
的图像,并直接写出函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8b735d48d94f66560e70a3455d6a12.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(3)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
定义
上的偶函数,当
时,
,
(1)在图中画出函数
的图像并根据图像写出函数
的单调增区间;
(2)求
的解析式;
(3)求不等式
的解集.
![](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/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/5dd79d5f-4e2b-41da-9db3-73215ba914db.png?resizew=188)
(1)在图中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a33661bff1e5e33951b4783b24a994.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)在直角坐标系
下,画出函数
的草图(用铅笔作图);
(2)写出函数
的单调区间;
(3)若关于
方程
有
个解,求
的取值范围(直接写出答案即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5399eee71383eec4ae5b92b817ee430b.png)
(1)在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
是定义在R上的奇函数,且当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/31d79b83-4816-4ef4-b966-bb628f8dfb1a.png?resizew=194)
(1)求出当
时,
的解析式;
(2)如图,请补出函数
的完整图象,根据图象直接写出函数
的单调递减区间;
(3)结合函数图象,求当
时,函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15308be822e4af7bc4054e7aa4c50e80.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/31d79b83-4816-4ef4-b966-bb628f8dfb1a.png?resizew=194)
(1)求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)如图,请补出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)结合函数图象,求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0c8c40d3b0b4d5cd85852959249dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
您最近一年使用:0次
2023-12-12更新
|
166次组卷
|
2卷引用:北京市丰台区怡海中学2023-2024学年高一上学期期末模拟练习数学试题