解题方法
1 . 对于函数
,函数图象上任意一点A关于点P的对称点
仍在函数图象上,那么称点P为函数图象的对称中心.如果
足够大时,图象上的点到直线
的距离比任意给定的正数还要小,那么称函数图象无限趋近于该直线
,也称直线
是函数图象的非垂直渐近线.
(1)研究函数
的性质,填表但无需过程:
(2)根据(1),在所给的坐标系中,画出大致图象,如有对称中心,则在图象中标为点P,如有非垂直渐近线,用虚线画出;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/9666ea8a-c948-4c6b-87d0-fb09cc31a56f.png?resizew=288)
(3)由(1)(2),选择以下两个问题之一来答题.
①如果函数
的图象有对称中心,请根据题设的定义来证明,如果没有,请说明理由;
②请根据题设的定义,证明:函数
的图象在x轴上方,且无限趋近于x轴,但永不相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe916d05211cf74a2b1428a8bb8bbbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)研究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7c3338bd45a8a412b672118e8aea7d.png)
值域 | |
单调性 | |
奇偶性 | |
图象对称中心 | |
图象非垂直渐近线 |
(2)根据(1),在所给的坐标系中,画出大致图象,如有对称中心,则在图象中标为点P,如有非垂直渐近线,用虚线画出;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/9666ea8a-c948-4c6b-87d0-fb09cc31a56f.png?resizew=288)
(3)由(1)(2),选择以下两个问题之一来答题.
①如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
②请根据题设的定义,证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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2 . 设
是定义在
上的函数,若存在两个不等实数
,使得
,则称函数
具有性质
,那么下列函数:
①
;②
;③
;
具有性质
的函数为_____ (填写所以正确答案的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a0bb446cb6e4f85b1a5c9fb489eedb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb1fe0741a0b3ffa49c2eff0efb443b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ebdc4d97e166405362b400d54f0903.png)
具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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3 . 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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解题方法
4 . 已知
(
为常数),对任意
,均有
恒成立,下列说法:
①
的周期为6;
②若
(
为常数)的图像关于直线
对称,则
;
③若
,且
,则必有
;
④已知定义在
上的函数
对任意
均有
成立,且当
时,
;又函数
(
为常数),若存在
使得
成立,则实数
的取值范围是
,
其中说法正确的是_______ (填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7128d1a3fe71da1a5fdc2315a0f805fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef94a6b9016d43e325aa8a6024f76c3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d99cf5d99140e960651e0f08f44b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d40aae4110ea16d0c869a135dcf6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55560cd5fe39382cbca04868146d86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fdff0b060d6161c448aa877ea303.png)
④已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7db6eef9f5bfb4403cb3e0eddf341b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606fd3966dc72e0f8a32047945a86e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde1d028eebbd57688f9ab7726d88d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eec8cb2cd9b83123c5e63792abcb810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbef9c98c3345729167cbc959ec23554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4446726305e3f696afb2e410f466aabd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9746cd5bbff4b4cd84904d3c0b3519c.png)
其中说法正确的是
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5 . 据历史记载,美日在中途岛(Midway)海战前,美方截获了日方密码电报,据美方已破译的密码得知,日方将向某岛进行军事活动,但关键含有地点的部分却被日方换成了另一种密码.经专家研究,估计是一种密匙密码,且密匙为3位.所谓密匙密码是指:将一段英文字母的明文(未加密前原文)经过对某一组数字(即密匙)的变换,改变成了另一组英文字母成为密文(加密后的文字)例如:明文:
(不计空格,不计大小写)在密匙为:1 9 2的条件下,变换过程如下图所示:
则密文为:
,试根据上面信息回答下面问题:
(1)在密匙为111的条件下,填写下表,并写出密文;
密文____________________.
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15de042ebf4d454a087d9d7245b0b2.png)
请填写下表,并写出密匙;
密匙为_____________.
(3)若下面即是那段包含地点(Midway)的破译不出的密文:
,且此段密文也是3位密匙加密,试填写下表,写出密匙,并将此段密文翻译成明文.(不必证明,写出明文即可)
密匙为___________,明文为_________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1199c50aa9f4377250cb26bc3724e0.png)
s | t | u | d | e | n | t |
1 | 9 | 2 | 1 | 9 | 2 | 1 |
t | c | w | e | n | p | u |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4ce1ed5abff05c5609344896eac946f.png)
(1)在密匙为111的条件下,填写下表,并写出密文;
s | t | u | d | e | n | t |
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15de042ebf4d454a087d9d7245b0b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ab9a53020088b09879ececa7bee1ad.png)
s | t | u | d | e | n | t |
(3)若下面即是那段包含地点(Midway)的破译不出的密文:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1be7cf9cfde23043448eabb187e10c.png)
c | w | b | c | f | s | o | l | l | y | d | g |
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6 . 在下面的坐标系中画出下列函数的图像:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/d7887848-146f-493a-b70f-0ef36c6c6418.png?resizew=200)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/44b6ca28-77a3-4880-85dd-01d56250e211.png?resizew=197)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175da291995b66f7a5e4e770062fbaba.png)
(2)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/d7887848-146f-493a-b70f-0ef36c6c6418.png?resizew=200)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/44b6ca28-77a3-4880-85dd-01d56250e211.png?resizew=197)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175da291995b66f7a5e4e770062fbaba.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c227bb1fbfa452b7c5b618236f9bddf4.png)
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解题方法
7 . 已知函数
是定义在
上的奇函数,且
图象如图所示.
(1)根据奇函数的对称性,在如图的坐标系中画出
时图象;
(2)①求当
时,
的解析式;
②说明当
时,
的单调性并用单调性定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3549d9f830745a7408e1c3c1cb3c29a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/05a53d47-2ce9-4987-8317-f8ac4d606c0d.png?resizew=168)
(1)根据奇函数的对称性,在如图的坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
(2)①求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
②说明当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc95bc46e0aa25342600533d9a6082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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解题方法
8 . 已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/d5e3b8af-c1d6-4e55-934a-4db033eea223.png?resizew=214)
(1)判断并证明函数
的奇偶性;
(2)判断并证明函数
在区间
上的单调性;
(3)根据函数
的性质,画出函数
的大致图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1798b9e950a7764b6e908c3f4bb22b40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/d5e3b8af-c1d6-4e55-934a-4db033eea223.png?resizew=214)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
(3)根据函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
2023-03-10更新
|
483次组卷
|
6卷引用:上海市金山区2022-2023学年高一上学期期末数学试题
上海市金山区2022-2023学年高一上学期期末数学试题上海市金山区2022-2023学年高一下学期3月统考数学试题(已下线)黄金卷03(已下线)3.2.2 函数的奇偶性(精讲)-《一隅三反》(已下线)期末真题必刷基础60题(25个考点专练)-【满分全攻略】(沪教版2020必修第一册)(已下线)第5章 函数概念与性质 章末题型归纳总结 (1)-【帮课堂】(苏教版2019必修第一册)
解题方法
9 . 圆周率π的定义为:圆的周长与其直径之比,魏晋数学家刘徽注疏《九章算术》时,采取了增加圆的内接正多边形的边数,用正多边形周长逼近圆周的方法求π的近似值.
(1)据此,在单位圆内构造恰当的内接正多边形,证明:
;
(2)试借助计算器,列表描点,在直角坐标系中画出大致图象,描述函数
在区间D上的单调性,不必证明.根据D的不同情况,任选下列一题作答(都做的话,只选前者评分).
①
;
②
;
(3)根据(1)(2)证明:
.
(1)据此,在单位圆内构造恰当的内接正多边形,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7b90758b160fde273f833c0ead73b5.png)
(2)试借助计算器,列表描点,在直角坐标系中画出大致图象,描述函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa332d83f2f258a49d0636279be11a6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169ab597aa0807cacbcf52fad1efa63a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c8a116f962ae769863da8cf8e8b1b3.png)
x | |||||||||
![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc7d795a5b254d956664cb8335aaa31.png)
您最近一年使用:0次
解题方法
10 . 已知函数
;
(1)求函数
的定义域;
(2)判断函数
的奇偶性、单调性;(不必证明)
(3)画出函数
的图像;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675f18f3547ef8cd757a0d1642a3173a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次