1 . 已知函数
,若函数
所有零点的乘积为1,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00660a23d34b28bff918675016329a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063e117674cfa096c5f0aa45f7d663d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-17更新
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2卷引用:山东省日照市2023-2024学年高一上学期期末校际联合考试数学试题
名校
解题方法
2 . 已知
表示不超过
的最大整数,例如:
,
.定义在
上的函数
满足
,且当
时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3821a8de1951d6fe6bcf05ed0fedb586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239da0d432f374cbd47bbcc3f120bc6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cc0ada3e13a381c1d4186d239ebcf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58bbbdde60cf4f80c3ea6a1740edba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdbb1aa709e3afe2a9afdd8957768438.png)
A.![]() |
B.当![]() ![]() |
C.![]() ![]() |
D.关于![]() ![]() ![]() |
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2卷引用:福建省厦门市2023-2024学年高一上学期1月期末质量检测数学试题
3 . 设函数
(
且
).给出下列四个结论:
①当
时,方程
有唯一解;
②当
时,方程
有三个解;
③对任意实数a(
且
),
的值域为
;
④存在实数a,使得
在区间
上单调递增;
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf1a29518ba7fb41a351ae69ce43c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342d52fc26cc550a45b80756903bee6.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e436ea3ddcd13e69171135f0ff8e934a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342d52fc26cc550a45b80756903bee6.png)
③对任意实数a(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
④存在实数a,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
其中所有正确结论的序号是
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4 . 已知函数
,
.
(1)若
,求函数
的值域;
(2)若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539984081c2472e81c91e61fe87b4c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0eef90b394d3e1f7047aa8746f4f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知函数
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c78628a2dab558e80b4fccca5e287ea.png)
A.若函数![]() ![]() ![]() ![]() |
B.若函数![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若函数![]() ![]() ![]() ![]() |
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2卷引用:安徽省部分重点中学2023-2024学年高一上学期期末测试数学试卷
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6 . 已知定义在
上的函数
,对任意的
,都有
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146ff57d46a7f258604e9660a726fdba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b6c58f9bcbbcf99ba037e3bd4497a.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
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7 . 设
,
,若
在
上是增函数且
在R上至少有3个零点,则a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73fd0fb19d355e5b439ab02051d3384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4095a2eeca51283e5f28c156c8eae0dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae702c7fac150ca5052d2eb88ee0dfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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8 . 函数
的定义域为
,若对于任意的
,当
时,都有
,则称函数
在
上为非减函数.设函数
在
上为非减函数,且满足以下三个条件:①
;②
;③
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc1bc250c8a6523a1be394ff48d4a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ee7abd882ba99660bca68ebf544cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ca42f5662e7b0e3f355995c5afcdec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4353063dd9040af707cf28416c5f03bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afdc66f3e598a970f2236f7052a573b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
9 . 已知函数
.
(1)证明函数
的图象过定点;
(2)设
,且
,讨论函数
在
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84117b58944d6788691c2b24c070bb47.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71badab736269c6567a3977823e2f9b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f999c9cba4a1a083959709371447.png)
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4卷引用:重庆市2023-2024学年高一上学期期末联合检测数学试卷
重庆市2023-2024学年高一上学期期末联合检测数学试卷重庆市2023-2024学年高一上学期期末数学试题福建省厦门市第一中学2023-2024学年高一上学期期末模拟数学试题(已下线)4.4.2对数函数的图象与性质(第3课时)
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e63f5e55fa52bfd33b893b43450f80e.png)
(1)已知函数
,若方程
在
上有四个不相等的实数根,求:实数
的取值范围;
(2)若函数
的定义域为
,求:函数
的最值;
(3)
,不等式
恒成立,求:实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e63f5e55fa52bfd33b893b43450f80e.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4866901bf4c72adda935fddce76ed10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6edcd14735d5ffc686caf41bbbe91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9af3016ebe0c067782b2e6ef771c955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3475f7a186b113ceac3a918d20e238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8b67c150cb8f83b41f8ecf1d5ee0fc.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0be5ff925023d33f7305c204a22243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf384a5fc8e162385160a4f79bd638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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