1 . 已知函数
(
,
).
(1)若
时,判断函数
在
上的单调性,并说明理由.
(2)若对于定义域内一切x,
恒成立,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448fe7d74715fe777821c054977c959f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
(2)若对于定义域内一切x,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13eb1542c4f359eac4452862aebbb31c.png)
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解题方法
2 . (1)已知
;求
(用含
的式子表示)
(2)已知
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3048ed635f43cb0651cf370db7b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4d7f1e9464efa2d799958d85e76647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776645d0a2952471ce07c9ffb9eea18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 已知函数
的定义域为A,值域为B.
(1)当
时,求集合A;
(2)当
时,求集合B.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8fda1cdb1b267da1fc884c4979fd59.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
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23-24高一上·上海浦东新·期中
名校
4 . 已知两条水平直线
:
和
:
(其
),且直线
与函数
的图象从左至右相交于点A、B,直线
与函数
的图象从左至右相交于点C、D.若记线段AC和BD在x轴上的投影长度分别为a、b(投影点重合时长度为0).
(1)记点A、B、C、D的横坐标分别为
、
、
、
,求证:
;
(2)当
时,求m的值;
(3)当
,m变化时,记
,求函数
的解析式及其最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6614af916b2555d13e82d318736724d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f7701bfbb74039de04042baa9c1679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952693f4e982e17a9658ca2cb1b534e6.png)
(1)记点A、B、C、D的横坐标分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c97938d07092ac2803ff89a47e5b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0189322d31e9b630ab0c0df14aa030a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6c00cb2047fdede2e5a46d83a6a411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d6ab4479fca30268660739ec6852c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9219f535c2a796f525758866257fbb3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9dbe6d2509fab2a9c276a5de980bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cdf4eb677e6651ae7650cccce15ffb.png)
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2023-11-13更新
|
233次组卷
|
5卷引用:上海市华东师范大学第二附属中学2023-2024学年高一上学期期中数学试题
(已下线)上海市华东师范大学第二附属中学2023-2024学年高一上学期期中数学试题(已下线)第四章 幂函数、指数函数与对数函数(常考必刷30题10种题型专项训练)-【满分全攻略】(沪教版2020必修第一册)(已下线)专题01幂函数、指数函数与对数函数全章复习攻略与难点强化训练(2)-【寒假自学课】(沪教版2020)(已下线)专题12对数函数-【倍速学习法】(沪教版2020必修第一册)(已下线)模块四专题4 大题分类练(对数函数及其应用)拔高提升练(人教A)
名校
解题方法
5 . 已知函数
,其中常数
且
.
(1)判断上述函数在区间
上的单调性,并用函数单调性定义证明你的结论;
(2)若
,利用上述函数在区间
上的单调性,讨论
和
的大小关系,并述理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8031111194dc972dc070cbbfe328e208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)判断上述函数在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109d06b8be2e402b5ffbb0aeb501009.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109d06b8be2e402b5ffbb0aeb501009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6058504673152a7be9d1c55bde2a06.png)
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6 . 已知函数
是奇函数.
(1)求实数
的值;
(2)当
,
,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6963114091fa47a246cde471ca2afd7.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ca7004a9e660fa07eb0eb98c14322.png)
您最近一年使用:0次
名校
7 . 已知
,
(1)当
,求
的值;
(2)当
时,用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e0cb283176f823366889529c134a95.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6c19345b73e5da64a402d4bfe581e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cc033406da2cdd342308972c6701f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2af6c72c04da8cf2d83f2f8aa902659.png)
您最近一年使用:0次
2023高一·上海·专题练习
解题方法
8 . 已知
是偶函数.
(1)求实数
的值;
(2)证明函数
在
上的单调性,解不等式
;
(3)记
,若
对任意的
都成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0a94a7bdfb575b165cbafab6a548a7.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d033362b3777e7abf16e6286495c10c.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee5265f1a9ed70f3eb1133438d73b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2c01ac2a7f6ad7e03cb7a61daefab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023高一·上海·专题练习
解题方法
9 . 已知函数
.
(1)解不等式
;
(2)求函数
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c04cd03ce275e28626235b657d1fb71.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
解题方法
10 . 已知函数
,设
.
(1)当
时,解关于
的不等式
;
(2)对任意的
,函数
的图象总在函数
的图象的下方,求正数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bac74808b9877e551f39ce57d5f41b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ad4b6efae29ab7dec69eedf348eaa0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e02125e0a1f3cda39742b765baa74c.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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