1 . 已知函数
,
(1)若
,函数
在区间
上单调递增,求
的取值范围;
(2)若
,
,求函数
在
上的值域;
(3)若
,函数
在
内没有对称轴,求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d58ebc68f8481976fdcbf3535c4527.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590e165e407098fcac9f871beb047dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a908cff3963ed5281930402c853b0b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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名校
2 . 已知
,其中
,满足以下三个条件:(1)函数
的最小正周期为
;(2)函数
的图象关为直线
对称;(3)函数
在
上是严格减函数.则函数
的表达式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4f29a473e9757d8f24f627f52e9e15.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ca1100b456583c791b802ea0b12cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92db0e98ec7642e59d61273a9182d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785402fa07a9da57855f71551c4f0d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4f29a473e9757d8f24f627f52e9e15.png)
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名校
3 . 已知
,其中
.若函数
在区间
上有且只有一个最大值点和一个最小值点,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6517ab3e70d42d196d749465734651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c3c33511e59ff6e2f8078de2f06ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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2024·全国·模拟预测
4 . 已知函数
,若
的图象在
上有且仅有两条对称轴,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611792520f93bc93445492610823eac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4b61d912f99e5583e7e17cf8fef558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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5 . 函数
的相邻两条对称轴之间的距离为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c84ed64c92bf82ddc2aede49bb7b8f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
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名校
6 . 已知函数
的初始相位为
,若
在区间
上有且只有三条对称轴,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308f2fc52806de20486b103d3fffdebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知函数
.
(1)某同学打算用“五点法”画出函数
再某一周期内的图象,列表如下:
请填写上表的空格处,并写出函数
的解析式;
(2)若函数
,将
图象上各点的纵坐标不变、横坐标扩大到原来的2倍,再向右平移
个单位,得到函数
的图象,若
在
上恰有奇数个零点,求实数a与零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e613ec74a2f330b57a235439510dc5.png)
(1)某同学打算用“五点法”画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
x | ![]() | ![]() | ![]() | ||
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | 1 | 0 | ![]() | 0 |
![]() | 0 | ![]() | 0 | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfa338e78c528663f0602c60f3f594d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdb2704ea6bc44b5a75fb3c8a100353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aab44d48c65864b1f46ea3647437bbe.png)
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8 . 若将函数
向右平移
个单位后其图像关于
轴对称,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e1e06a5c38da7a25d7c42c8f252b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
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2023-11-05更新
|
452次组卷
|
2卷引用:上海市华东师范大学第二附属中学2023-2024学年高一下学期期中考试数学试题
9 . 已知
,若函数
的图象关于
对称,且函数
在
上单调,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674f866fb89ea7d56186ea6ff87a8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3038a4b8c02b12b821fbd0fd69145900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dff5b63913762b3be82e55a18f3847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
A.4 | B.3 | C.2 | D.1 |
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解题方法
10 . 已知函数
(
),其图像的一个对称中心是
,将
图像向左平移
个单位长度后得到函数
的图像.若对任意
,当
时,都有
,则实数
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e1df15aec5b2220a939bf5c2b23163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb61a448347a3f8c1f126d1c00730cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d23b5869cdc1003db52838abfd86e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d1308d5db144e31b4d0211c63ef52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c765386a72600b7cb1edefeebf85178e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c988a59ec5a5d61172025c66b713a4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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