1 . 如果函数
满足:对于任意
,均有
(m为正整数)成立,则称函数在D上具有“m级”性质.
(1)分别判断函数
,
,是否在R上具有“1级”性质,并说明理由;
(2)设函数
在R具有“m级”性质,对任意的实数a,证明函数
具有“m级”性质;
(3)若函数
在区间
以及区间
(
)上都具有“1级”性质,求证:该函数在区间
上具有“1级”性质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc1bc250c8a6523a1be394ff48d4a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079957ae49da067d35085e6ce81ff8f3.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0089d9b39592e2eef4c486c5055648d7.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e682f89425146ac9cb16b2f13a014c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819123c00dd8547948fd6a142d23eb8.png)
您最近一年使用:0次
解题方法
2 . 在数学中,不给出具体解析式,只给出函数满足的特殊条件或特征的函数称为“抽象函数”.我们需要研究抽象函数的定义域、单调性、奇偶性等性质.对于抽象函数
,当
时,
,且满足:
,均有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367936b458618efb6b2eadc843e5d6ba.png)
(1)证明:
在
上单调递增;
(2)若函数
满足上述函数的特征,求实数
的取值范围;
(3)若
,求证:对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6571b33b56c6cd88f2f6e091031bcf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367936b458618efb6b2eadc843e5d6ba.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c5f8b7a1a268c904d04356f0d1b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be9b79f42bbf0de1851607050c3e8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219598f1289ddb370d632ea141731d52.png)
您最近一年使用:0次
3 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线.1691年,莱布尼茨等得出“悬链线”方程
,其中
为参数.当
时,就是双曲余弦函数
,类似地我们可以定义双曲正弦函数
.它们与正、余弦函数有许多类似的性质.
(1)类比正弦函数的二倍角公式,请写出双曲正弦函数的一个正确的结论:
_____________.(只写出即可,不要求证明);
(2)
,不等式
恒成立,求实数
的取值范围;
(3)若
,试比较
与
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852665ec9c3a65b758898059361f11a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a7c1d3681898e25187a896aeb0c8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0718c04bdf70989bcc90b902671a692.png)
(1)类比正弦函数的二倍角公式,请写出双曲正弦函数的一个正确的结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8fe1e65b09697538d4dee0746846f4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe9f3099ed9429dc5b4e38a350e524a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343e7c30c2a5d166819b28e23fad2203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563f464c94feac28033f6f3a271fbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2cebaab3423dfb2f2c944dfc43df8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb966b7b2dd6581640bcee2d97dacf77.png)
您最近一年使用:0次
2024-01-27更新
|
930次组卷
|
8卷引用:福建省宁德市2023-2024学年高一上学期1月期末质量检测数学试题
福建省宁德市2023-2024学年高一上学期1月期末质量检测数学试题(已下线)专题04 三角函数恒等变形综合大题归类 -期末考点大串讲(苏教版(2019))河南省名校联盟2023-2024学年高一下学期3月测试数学试题(已下线)第八章:向量的数量积与三角恒等变换章末重点题型复习(2)-同步精品课堂(人教B版2019必修第三册)河南省信阳市信阳高级中学2023-2024学年高一下学期3月月考(一)数学试题(已下线)第8章:向量的数量积与三角恒等变换章末综合检测卷(新题型)-【帮课堂】(人教B版2019必修第三册)重庆市缙云教育联盟2024届高三下学期2月月度质量检测数学试题(已下线)压轴题函数与导数新定义题(九省联考第19题模式)讲
4 . 已知函数
,
,若存在常数k(
),使得对定义域D内的任意
(
),都有
成立,则称函数
在其定义域D上是“k-利普希兹条件函数”
(1)判断函数①
,②
是否是“1-利普希兹条件函数”,若是,请给出证明;若不是,请说明理由;
(2)若函数
(
)是“k-利普希兹条件函数”,求常数k的最小值;
(3)若
是定义在闭区间
上的“2-利普希兹条件函数”,且
,求证:对任意的
都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ecdccf4a334ea959a456533c40d53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)判断函数①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef469c7b7cb9945b984222381b9c000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6ad6387d592102a743742620eee7fe.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d0c9d13770863f59ea9fa45488de63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6c0fddb9074dfc96be03b4aa24d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a8c69aaecfbe4d8bd7cf01a3b79c50.png)
您最近一年使用:0次
5 . 已知函数
的定义域为
,
为大于
的常数,对任意
,都满足
,则称函数
在
上具有“性质
”.
(1)试判断函数
和函数
是否具有“性质
”(无需证明);
(2)若函数
具有“性质
”,且
,求证:对任意
,都有
;
(3)若函数
的定义域为
,且具有“性质
”,试判断下列命题的真假,并说明理由,
①若
在区间
上是严格增函数,则此函数在
上也是严格增函数;
②若
在区间
上是严格减函数,则此函数在
上也是严格减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803b4afffc6c71c6d2c3d8dff0102189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57e815c01a412466a6aa12d3e883a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a3c7303b5dccb55a94db4abb410932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64646b34d48e913836a220e24460734.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
您最近一年使用:0次
2023-01-12更新
|
618次组卷
|
6卷引用:上海市闵行区2022-2023学年高一上学期期末数学试题
上海市闵行区2022-2023学年高一上学期期末数学试题(已下线)专题10 指数及指数函数压轴题-【常考压轴题】(已下线)第五章 函数的概念、性质及应用(压轴必刷30题9种题型专项训练)-【满分全攻略】(沪教版2020必修第一册)(已下线)期末真题必刷压轴60题(10个考点专练)-【满分全攻略】(沪教版2020必修第一册)(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第四章 指数函数与对数函数-【优化数学】单元测试能力卷(人教A版2019)
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeccfff03711ca585eb358459dc68107.png)
(1)求证:用单调性定义证明函数
是
上的严格减函数;
(2)已知“函数
的图像关于点
对称”的充要条件是“
对于定义域内任何
恒成立”.试用此结论判断函数
的图像是否存在对称中心,若存在,求出该对称中心的坐标;若不存在,说明理由;
(3)若对任意
,都存在
及实数
,使得
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeccfff03711ca585eb358459dc68107.png)
(1)求证:用单调性定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8319f56cfb802b0e049b4765b5ec79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4003115706a191f2d4415119e73ddaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9902484b765fe634029040cc5dae6cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8ef8cdf661a9557e490588ef45dcfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
7 . 设
,函数
.
(1)若
,求证:函数
是奇函数;
(2)若
,判断并证明函数
的单调性;
(3)设
,
,若存在实数m,n(
),使得函数
在区间[m,n]上的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d04bcc342e046321abc203690916602.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45cf196f21e10ce4031d26fefc22f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2022-01-21更新
|
713次组卷
|
8卷引用:江苏省南通市通州、海安2019-2020学年高一上学期期末联考数学试题
江苏省南通市通州、海安2019-2020学年高一上学期期末联考数学试题(已下线)【新东方】在线数学35上海市控江中学2021-2022学年高一上学期期末数学试题江苏省南通市通州区金沙中学2020-2021学年高一上学期第二次调研考试数学试题四川省四川师范大学附属中学2021-2022学年高一上学期12月月考数学试题(已下线)第13讲 函数的基本性质(8大考点)(3)(已下线)第13讲 函数的基本性质(8大考点)(2)(已下线)专题14函数的基本性质-【倍速学习法】(沪教版2020必修第一册)
名校
解题方法
8 . 设函数
定义在区间
上,若对任意的
、
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177e54e8deea5da9dc6bc82eb3de0c2c.png)
,当
,且
时,不等式
成立,就称函数
具有M性质.
(1)判断函数
,
是否具有M性质,并说明理由;
(2)已知函数
在区间
上恒正,且函数
,
具有M性质,求证:对任意的
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
,且
,有
;
(3)①已知函数
,
具有M性质,证明:对任意的
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
,有
,其中等号当且仅当
时成立;
②已知函数
,
具有M性质,若
、
、
为三角形
的内角,求
的最大值.
(可参考:对于任意给定实数
、
,有
,且等号当且仅当
时成立.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9c587f6257331045c362ef25677c20.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/770cf3716f1e9dc8023a898df7f33783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177e54e8deea5da9dc6bc82eb3de0c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d589f18d16b1a6bbd5108409c53fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49c641617f38855f6abc7baf36af8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f05279fb93940ea0741b64227cc58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a70644524df044d4a24b998a81d44c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a20b276768b190ac15c9aa5c352ef.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9c587f6257331045c362ef25677c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fcd5a1ca4f9abf76c88db3a3542b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5348b540c0b2e012191ae95351aaac.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/9d589f18d16b1a6bbd5108409c53fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450fb41cf5543a06035606ff29a9e934.png)
(3)①已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5348b540c0b2e012191ae95351aaac.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d589f18d16b1a6bbd5108409c53fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f183be2a65b185fd240990dffdec3ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62e63003be4ad8c4c51e36e71df2ac3.png)
②已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e6e44271b4c08be46dda1e7403741.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8080fef9bdfa92ae70f3e314eef3e3.png)
(可参考:对于任意给定实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205ca5a7d5bede14db0175445bb6d508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6b79d363c080275b93b8cc4b279653.png)
您最近一年使用:0次
2021-12-27更新
|
696次组卷
|
5卷引用:专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)
(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)上海市黄浦区2022届高三一模数学试题(已下线)上海市黄浦区2022届高三上学期一模数学试题(已下线)第04讲 函数最值与性质-3上海市文来高中2023届高三上学期期中数学试题
名校
解题方法
9 . 设函数
的定义域为
.若存在常数
,
,使得对于任意
,
成立,则称函数
具有性质
.
(1)判断函数
和
具有性质
?(结论不要求证明)
(2)若函数
具有性质
,且其对应的
,
.已知当
时,
,求函数
在区间
上的最大值;
(3)若函数
具有性质
,且直线
为其图像的一条对称轴,证明:
为周期函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809ea2eff71a0de3db640313ad25b7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404d068b60dd901194f1684d023212ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8073fa685bc10cf01a0128220feac940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e661ad31aa4c6d8684923cf904bf1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d0588454ec8b64bf86578fb90b39e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55351494cd96fed31976fdc5d9c7292.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2021-08-01更新
|
572次组卷
|
3卷引用:北京市西城区2020-2021学年高一下学期期末数学试题
名校
10 . 设函数
的定义域为R.若存在常数
,对于任意
,
成立,则称函数
具有性质
.记P为满足性质
的所有函数的集合.
(I)判断函数
和
是否属于集合P?(结论不要求证明)
(II)若函数
,证明:
;
(III)记二次函数的全体为集合
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41b8856f1acaf13e6968f0a96f37795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fdc23b0a70af927be89b9e89c3ab95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(I)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
(II)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8e5003f8ca5eb9e1ad0e5acd6ce910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd26997a82d0638e76cd0fd3c31a57a2.png)
(III)记二次函数的全体为集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc887a6c34c3e2f859e6a59a9ed4cac7.png)
您最近一年使用:0次
2021-01-26更新
|
703次组卷
|
3卷引用:北京市西城区2020-2021学年高一上学期期末考试数学试题