1 . 已知函数
的定义域为D,对于D中任意给定的实数x,都有
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd191eb816068d98b105eb3a08a516f2.png)
.则下列3个命题中是真命题的有_____________ (填写所有的真命题序号).
①若
,则
;
②若当
时,
取得最大值5,则当
时,
取得最小值
;
③若
在区间
上是严格增函数,则
在区间
上是严格减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf26cb0612e3afd9fe70bbfa46975c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd191eb816068d98b105eb3a08a516f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ef6845a8d115227494c3039d55eeb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
②若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
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名校
解题方法
2 . 函数
在______ 单调递增(填写一个满足条件的区间).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d8380fd0dd90da4a0e488ddc2fe5fd.png)
您最近一年使用:0次
2022-01-21更新
|
427次组卷
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3卷引用:浙江省衢州市2021-2022学年高一上学期期末教学质量检测数学试题
3 . 函数
在区间
上的单调性是______ .(填写“单调递增”或“单调递减”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b13989845b4476997ec735fc8ea4524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
2022-03-13更新
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791次组卷
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2卷引用:天津市河北区2021-2022学年高一上学期期末数学试题
名校
4 . 若函数
在定义域
内满足:对任意的
,
,
且
,有
,则称函数
为“类单调递增函数”.下列函数是“类单调递增函数”的有填写所有满足题意的函数序号).__________ .
①
;②
;③
;④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ed8a3eb8fc3fa0d2e6ff6b4f50e873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89edc5d98eb1743b3ae10e1128af258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de9d443a9fcc1fa6d79ba46c90a5a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b780670b99e950a0f529dc58190648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9a16664ad088899f6437b9637b80b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ab2ab03be596b8b6ad32cf52f82169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376f99f4ea973cddfc5e759455aefe34.png)
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2020-10-25更新
|
271次组卷
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6卷引用:河南省2020-2021学年高中毕业班阶段性测试(二)理科数学试题
5 . 如果函数
满足在集合
上的值域仍是集合
,则把函数
称为H函数.例如:
就是H函数.下列函数:①
;②
;③
;④
中,______ 是H函数(只需填写编号)(注:“
”表示不超过x的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5de9c4ca739b182a9c449c262276570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5de9c4ca739b182a9c449c262276570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e212cdbfba6610bc55df2c1a737407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd6674988e75e51f16f42fa1778d0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8219ac3bf37574ded5ec32f8ebcb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
您最近一年使用:0次
6 . 某同学探究函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
的最小值,并确定相应的x的值.先列表如下:
请观察表中y值随x值变化的特点,完成下列问题:((1)(2)问的填空只要写出结果即可)
(1)若
, 则
.(请填写“
, =,
”号);若函数
在区间 (0,2)上递减,则
在区间 上递增;
(2)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
的最小值为 ;
(3)根据函数
的有关性质,你能得到函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5effb3053cf609f59178641cd48167.png)
的最大值吗?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118c9c0597d2c72126fbc4cc3927108e.png)
x | … | ![]() | ![]() | 1 | ![]() | 2 | ![]() | 4 | 8 | 16 | … |
y | … | 16.25 | 8.5 | 5 | ![]() | 4 | ![]() | 5 | 8.5 | 16.25 | … |
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdfb7f9b4a4e8898702a030c5981dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915b3d29d0c7dd83c188e3ce31f52fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be22faef62e7a035eb39a2e020c880e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a009fc98a713bd1f25d427a02322464d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118c9c0597d2c72126fbc4cc3927108e.png)
(3)根据函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5effb3053cf609f59178641cd48167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e970b5a89849b870c50b39e97ee3bdf2.png)
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7 . 集合
,集合
,下列
,
间的关系:①A为B的真子集;②B为A的真子集;③
,其中正确的是___________ .(填写相应序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c3ea9ce901a68a64a6c0e8662e718b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0ca4023be6da8f1574b3b1ee8bffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
您最近一年使用:0次
2020-10-23更新
|
477次组卷
|
4卷引用:山东省济宁邹城市第一中学2020-2021学年高一10月月考数学试题
名校
8 . 已知定义在
上的函数
,有下列说法:
(1)函数
满足
则函数在
上不是单调减函数;
(2)对任意的
函数
满足
则函数在
上是单调增函数;
(3)函数
满足
则函数
是偶函数;
(4)函数
满足
则函数
不是奇函数.
其中,正确的说法是________ (填写相应的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf204e8357b7b74b7056c17aba7d4d9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041cd2291ceed0733b7a1baa3e3d740e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928fdf8d1c1289b1a4de1975152b6537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928fdf8d1c1289b1a4de1975152b6537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
其中,正确的说法是
您最近一年使用:0次
解题方法
9 . 已知
表示不超过
的最大整数,定义函数
.有下列结论:
①函数的图象是一条直线;②函数
的值域为
;
③方程
有无数个解;④函数是
上的增函数.
其中错误的是______ .(填写所有错误结论的序号)
![](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/602c6c52cae281dc7dad9bc7cc07d6bb.png)
①函数的图象是一条直线;②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fc9e0dce53875ba108a4a041fcbf1a.png)
③方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad56942439368d413f74e0ab7d9fb23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
其中错误的是
您最近一年使用:0次
2020-12-02更新
|
366次组卷
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3卷引用:山西省太原市2020-2021学年高一上学期期中质量监测数学试题
名校
10 . 在整数集Z中,被5除所得余数为k的所有整数组成一个“类”,记为
,即
,
.给出如下四个结论:
①
;
②
;
③
;
④整数a,b属于同一“类”的充要条件是“
”.
其中正确结论有____________ (填写正确结论标号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef3ae0a4507f1f66d5bf885a6b90d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab0cb11408747d29e4390131e8371f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63702e21678ae8a609cfa1faeef69fa6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992df7e0fb9f11450c44923ad41ab920.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2a818d5f8da20f51bde5f368de6f5e.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7564a88c692fa7ebe56747ae86824bfe.png)
④整数a,b属于同一“类”的充要条件是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fdc4deaa59b7ac4cc8bd4eaa8eecf4.png)
其中正确结论有
您最近一年使用:0次
2020-10-24更新
|
319次组卷
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3卷引用:江苏省苏州中学2020-2021学年高三上学期10月月考数学试题