名校
1 . 已知函数
.
(1)判断
在
上的单调性,并用定义证明:
(2)设
,若对任意的
,总存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6274a35c06ab2fce01792ba30781ddf.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a9e4d1e3248d61979ecbc60ff1ec44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1647deca74be1346f76ac07382917b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0cdf79ec49d52434473ee082eefc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2 . 已知函数
.
(1)求该函数的单调递增区间;
(2)若对任意![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c828f6dde5ccf7bce4520e961570883.png)
都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c90130a0dae10283091ba33c0cb6d24.png)
(1)求该函数的单调递增区间;
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c828f6dde5ccf7bce4520e961570883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05250abe6da85eb0b555948d7dbaf317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb808e08ba8d004f17759d626ca46cbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
解题方法
3 . 已知集合
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59edc8466620bc829277ae1fa17edaf.png)
(1)当
时,求
;
(2)在①
②
中任选一个作为已知,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6af87330d33120a8159477a2e17eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59edc8466620bc829277ae1fa17edaf.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b0cbfbb7f9547c3bdcc8356d456935.png)
(2)在①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbbe46a98a8fdebfc46fcbc45dc88e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b05d2be27e8f53e4de3071846dffb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
4 . 化简求值.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468e695ff8bdd1cb43f9c512f05d19a2.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468e695ff8bdd1cb43f9c512f05d19a2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a0a45740125f3e88eb6cf6f3999a59.png)
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5 . 已知函数
,相邻两对称轴之间的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
的值;
(2)若
时,方程
有解,讨论方程解的个数,若方程所有解的和记为
,求
所有可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f43285a39fa2bf73a37c9efdc80a989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd29544a6b056940d248c2fa4ec36043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c35393080972a7620f980c4f37d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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6 . 已知函数
的部分图象如图所示.
(1)求
的解析式及对称中心;
(2)先将
的图象横坐标缩短为原来的
倍,再向右平移
个单位后得到
的图象,求函数
在
上的单调减区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387ea7d2593a4e5b4781da1ffbb7ddc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/d118ca75-e053-48e3-8de1-e792835f2b13.png?resizew=153)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)先将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9773d20ecc287f7c16efdc655351680d.png)
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解题方法
7 . 已知函数
是奇函数.
(1)求实数
的值并判断函数单调性(无需证明);
(2)若不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4baecc93bc88af0709ec103355a49c84.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946244c9aaa1249364b1b5b5fa8c724f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
解题方法
8 . 近年来,合肥市地铁轨道交通高质量发展,成为中国内地轨道交通新星,便捷的交通为市民出行带来极大便利,刷新了市民幸福指数.春节将至,为了提升人们的乘车体验感,合肥某地铁线路准备通过调整发车时间间隔优化交通出行,已知地铁的发车时间间隔
(单位:分钟)满足
,通过调研,在某一时段,地铁载客量与发车时间间隔
相关,当
时地铁可达到满载状态,载客量为1250人,当
时,载客量会减少,减少的人数与
的平方成正比,且发车时间间隔为3分钟时载客量为610人,记地铁载客量为
.
(1)求
的解析式;
(2)经过对该线路的数据分析,得出市民乘车体验感指数
与发车时间间隔
之间的函数关系
,体验感指数越高,乘车体验感就越好,问当发车时间间隔为多少时,市民乘车体验感最好?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec68bc67ff0da0fbb4f0ec65cbec7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23394b35c0d74d62ec3d77c1aab8082e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b97d52702061dcfbca01195e99473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef66f1f47295c0d0fa734c9ecab72daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82a1224e47f31ecdfffd328d5a3ab6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82a1224e47f31ecdfffd328d5a3ab6d.png)
(2)经过对该线路的数据分析,得出市民乘车体验感指数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f058d3e6bcb988e7024f945de9d79c6.png)
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解题方法
9 . 已知函数
.
(1)求不等式
的解集;
(2)若对于
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeafd95bddad3cc3148adc5481c989fa.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e799c1971ec9b387e94d04fad4230e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-17更新
|
440次组卷
|
3卷引用:安徽省皖北六校2023-2024学年高一上学期期末联考数学试题
10 . 已知函数
为奇函数,且
图象的相邻两对称轴间的距离为
.
(1)求
的最小值.
(2)将函数
的图象向右平移
个单位长度,再把横坐标缩小为原来的
倍(纵坐标不变),得到函数
的图象,记方程
在
上的根从小到依次为
试确定
的值,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aacfe1700f79a16a1d0a40716446329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c67743ca66c91232cbccaf610542734.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d375e5567091ed4dd4320a77a4e36092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e83d59b0bfe4ddb1f9521109b5e0ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d5300bf9c70d22c587f733261047e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b570cf2353a62e6791cb1280ca398aae.png)
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