1 . 已知函数
(
,且
)是定义在R上的奇函数.
(1)求a的值;
(2)若关于t方程
在
有且仅有一个根,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571ce51eb32810277fb2fb9bd55a57bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d32d1a5a0732c7e4af737555e44ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求a的值;
(2)若关于t方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aade7468c98884534ab383a655a5f58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
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2卷引用:浙江省临平萧山学校2023-2024学年高一上学期期末数学试题
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2 . 已知定义在上的函数
满足:①
的图象关于直线
对称,②函数
为偶函数;③当
时,
,若关于x的不等式
的整数解有且仅有
个,则实数
的取值范围是
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3 . 已知函数
,其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1725be15f5b2a9410d6a2736095003e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
A.函数![]() |
B.若关于![]() ![]() ![]() ![]() |
C.方程![]() |
D.关于![]() ![]() |
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4 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9e17a5e76151b4aeccfaa023fb1efc.png)
A.函数![]() |
B.若函数![]() ![]() |
C.若关于![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.关于![]() ![]() |
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2024-03-21更新
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2卷引用:广西贺州市2023-2024学年高一上学期期末质量检测数学试题
5 . 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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6 . 已知函数
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6735e8606b9daa6c837601a6e13436.png)
(1)求
的解析式;
(2)设函数
,若方程
有
个不相等的实数解
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4198ff91032cc5fd1dced1c32a9acef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6735e8606b9daa6c837601a6e13436.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df08c7e96609ab0478c1c62650a87c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adabc767a9d3689906910ed308438870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d659d2026196c3b191a645df902ed0.png)
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解题方法
7 . 已知函数
有两个不同的零点,分别记为
,
,且
.
(1)求实数
的取值范围;
(2)若不等式
恒成立(e为自然对数的底数),求正数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e178299be0b5d8ebfe23963dc03d0521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.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/186d93ba36fde8219cd40ce9c0d7f531.png)
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8 . 已知函数
在区间
上单调,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32906d5d903b746760df451a828780c7.png)
______ ;函数
在区间
上恰有5个零点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a339581df8f5cec4b8abddb777e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37fb9ead0e9436b60bb8f82eaa64782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32906d5d903b746760df451a828780c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b929d10624c0bb2db150588694b9dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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9 . 已知函数
,若函数
有5不同的零点,则实数
的值可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557b0a241ef9a218711b14a7d218af55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add33a47cfb84d1140f852fa6e498f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:安徽省亳州市第二完全中学2023-2024学年高一上学期期末教学质量检测数学试题
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解题方法
10 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在
个不同的实数
,使得
(其中
),则称
为
的“
重覆盖函数”.
(1)判断
是否为
的“n重覆盖函数”,如果是,求出
的值;如果不是,说明理由.
(2)若
,为
,的“2重覆盖函数”,求实数
的取值范围;
(3)函数
表示不超过
的最大整数,如
.若
为
的“
重覆盖函数”请直接写出正实数
的取值范围(无需解答过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d5df7922a4e98e8e07bf418dd48a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d1a18f254577a0ce74ceb27364b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17efb86d82b9ddf50af4c23632a05c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e60e9c1e65686f8cd28a28abb8282c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f246e5b05b68bb9fdeb12a319aa7136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa88c20e58953bba4ed04d3ce419df95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ca781ffd5d55cc9b7dd551879ce65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4987dca9120f6a58139fd3e412ed77c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a899e901b141a0a6d56e3387ecf9f047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e946baf1316ac1f219398ecedadf6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:浙江省临平萧山联考2023-2024学年高二上学期期末数学试题