名校
1 . 函数
满足:当
时,
,
是奇函数.记关于
的方程
的根为
,若
,则
的值可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1092d77e2570be5584ebc0cdcdca2ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b08d939cee48042d0a565a53dbeadf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d500a74b865ade2b576720c04becd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed0b01191624fcc0469ecad0287a0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdb4c1ad5fce7cf952767c03b8eb6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.1 |
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2 . 设函数
定义域为
,如果存在常数
满足:任取
,都有
,则称
是
型函数,
是这个
型函数的
常数
(1)判断函数
,
是不是
型函数,并说明理由:如果是,给出一个
常数;
(2)设函数
是定义在区间
上的
型函数,
是一个常数,求证:函数
也是
型函数;
(3)设函数
是定义在
上的
型函数,其
常数
,且
的值域也是
,求
的解析式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc1bc250c8a6523a1be394ff48d4a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f3d630f52d4f0bed2203fd7902c61b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a54f5b19d3466b0fc4477c17dbec239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ff4b64f5aef4bed596c9c8177c9b73c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd380912d2e7a23501b7a48274040e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b006ca4156920323d4a6e5b824eb4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9ee8b106e2b5472e59f438a8882cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b006ca4156920323d4a6e5b824eb4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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名校
3 . 已知函数
图象上的点
均满足
对
有
成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d14c828a3f9835432279d83c6c331a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2db9a58e185e4fd9c4f86efb24480f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad5c8a4e4bad474651c0a61de820ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0440bb2a43a6f9669fb5c3703a024989.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
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4 . 下列四个结论中,正确的结论是( )
A.已知奇函数![]() ![]() ![]() |
B.已知函数![]() ![]() ![]() ![]() |
C.在区间![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
5 . 定义:集合
存在实数
,满足对任意的
,都有
恒成立
;集合
在
上是严格递增函数)
.
(1)若函数
,求实数
的取值范围;
(2)已知函数
,假设
,且
,试判断
的符号,并证明:
;
(3)若对任意函数
,满足
恒成立,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1763d903e56958b75774f1b8eb8603c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c210496ba4e7bfca7c6870fd1e7de4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca8bdc812627d925f00ed7c145d696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa985beb045f635b6eda71d7822bd19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca8bdc812627d925f00ed7c145d696.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bfc54d45a00d813a282637de0bd6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094d1c078988213a456751ca98c94445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0ab7094abfb9e6055e9d3386e03ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92eae618a85e2c63502ebff9ff7cb45f.png)
(3)若对任意函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a916025f7398e59efb3e67d5cc6dc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962dba16e9f5129df453497cee42266e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
6 . 下列选项正确的有( )
A.“![]() ![]() ![]() |
B.函数![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() |
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|
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22-23高三上·江西南昌·阶段练习
解题方法
7 . 黎曼函数R(x)是一个特殊函数,由德国数学家黎曼发现并提出,该函数定义在[0,1]上,当
都是正整数,
为最简真分数)时,
;当
或1或x为(0,1)内的无理数时,
.若
为偶函数,
为奇函数,当
]时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf51ef39626c5fbbca1cd931b4b19db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a507c062709cfe2f218896247461c7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35888de80226a81c4c80fecb8f4a9337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df21bcb07cb594d6614230b2317942f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb5e3c82f6a63eff281d22c5dce3717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55d54b37137bf7931c49d5ea0aa10d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa23f55b24e2c4f5d6fe25f577026a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f0938fdb2f573f102d3422eefb074e.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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(已下线)江西省南昌市金太阳大联考2023届高三上学期10月联考数学(文)试题(已下线)江西省南昌市金太阳大联考2023届高三上学期10月联考数学(理)试题贵州省毕节市金沙县2023届高三上学期期中教学质量检测数学(理)试题江西省南昌市三校(一中、十中、铁一中)2023届高三上学期第一次联考(11月)数学(理)试题
名校
解题方法
8 . 已知
,则关于函数
说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5780ea14b5cce76d74b5bf57014d94df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
A.函数![]() ![]() | B.函数![]() ![]() |
C.![]() ![]() | D.![]() |
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9 . 某校学习兴趣小组通过研究发现:形如
(
,
不同时为0)的函数图象可以由反比例函数的图象经过平移变换而得到,则对函数
的图象及性质,下列表述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34d59bd320be6a74f909ef313f94eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee8c7112fbe9ba6bb5b1ee10fee4e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bc5f0ef5e9129e22310d5ea17cf1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd15d2888d7f121ebce40d8519147f1.png)
A.图象上点的纵坐标不可能为1 |
B.图象关于点![]() |
C.图象与x轴无交点 |
D.函数在区间![]() |
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河北省唐县第一中学2022-2023学年高一上学期11月月考数学试题2023版 湘教版(2019) 必修第一册 过关斩将 第3章 函数的概念与性质第五章 函数概念与性质(A卷·能力提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第一册)河北省衡水中学2022-2023学年高一上学期期中数学试题(已下线)第3章 函数概念与性质(基础、典型、新文化、易错、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)3.3 函数的应用(一)(分层练习)-高一数学同步精品课堂(人教B版2019必修第一册)广东省佛山市顺德区容山中学2023-2024学年高一上学期期中数学试题(已下线)第三章 函数的概念与性质单元测试基础卷-人教A版(2019)必修第一册(已下线)专题03 函数的概念与性质1-2024年高一数学寒假作业单元合订本
10 . 定义在
上的连续函数
满足:对
,
,
,记
的导函数为
,
(
为常数);
(1)证明:
;
(2)设
,若
在
上恒成立,证明:
与
具有切点相同的公切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e837bb2555b79c3374f6c509c8fba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3276b5e12396fc4753eb3f8254f9fa68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eadf2473c62c7d838951afd5fbf5c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb85033fbe8df2901dcea9962f842a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b882352cacdeecd44c8344edc07fdc5d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb12c354506d18a9455e3fc154895b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2259e91a333ecf7900f6289f1fc22759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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