名校
解题方法
1 . 函数
的图象大致为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ef1fc49941cd3484ff53a738d4cd21.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-27更新
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2卷引用:贵州省毕节市金沙县2023-2024学年高一上学期期末质量监测数学试题
2 . 下列函数是偶函数的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-01-17更新
|
1794次组卷
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3卷引用:【市级联考】贵州省铜仁市2017-2018学年高一上学期期末监测数学试题
名校
3 . 下列函数中,既是偶函数,又在区间
上单调递增的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6ffa6fe2387ee19234c2ad0fcb92ea.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2021-01-23更新
|
766次组卷
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5卷引用:贵州省贵阳市普通中学2020-2021学年高一上学期期末监测考试数学试题
解题方法
4 . 定义函数
为“正余弦”函数.结合学过的相关知识,我们可以得到该函数的性质:
1.我们知道,正弦函数
和余弦函数
的定义域均为
,故函数
的定义域为
.
2.我们知道,正弦函数
为奇函数,余弦函数
为偶函数,对
,
,可得:函数
为偶函数.
3.我们知道,正弦函数
和余弦函数
的最小正周期均为
,对
,
,可知
为该函数的周期,是否是最小正周期呢?我们继续探究:
.可得:
也为函数
的周期.但是否为该函数的最小正周期呢?我们来研究
在区间
上的单调性,在区间
上,余弦函数
单调递减,正弦函数
在
上单调递增,在
上单调递减,故我们需要分这两个区间来讨论.当
时,设
,因正弦函数
在
上单调递增,故
,令
,
,可得
,而在区间
上,余弦函数
单调递减,故:
即:
从而,
时,函数
单调递减.同理可证,
时,函数
单调递增.可得,函数
在
上单调递减,在
上单调递增.结合
.可以确定:
的最小正周期为
.这样,我们可以求出该函数的值域了:显然:
,而
,故
的值域为
,定义函数
为“余正弦”函数,根据阅读材料的内容,解决下列问题:
(1)求该函数的定义域;
(2)判断该函数的奇偶性;
(3)探究该函数的单调性及最小正周期,并求其值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
1.我们知道,正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
2.我们知道,正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5562150b6fe45dc60e7790685d5cb0a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
3.我们知道,正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95905e2ad46af324ee4035edde8d69fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222443a4830f8e17589afbcd3b5ea8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987f14be6c8eafc1e87b74cbfc8ec724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268bc75afffcf150cd2d275d61d36db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d8084889c29e867974276d7f6cc476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f9e38660fee00a21e4216453cef349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab0957ab234a30417941f39466bb20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4718dc8a3682110b1eaf18c71f6411be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839783e6263b1078fb6ed58ea70091a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d47e9cb5749b486474f210c407afc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6895733d1e3b807a8d774ae70dc897e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987f14be6c8eafc1e87b74cbfc8ec724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35263c6f9845207fca5862101815e931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc02e7c12d8bec64f97adadbbf0e2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddde153cb6c0f7a212171b6b4bbf74ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2546805fbe7c56c33a7a91f3d9691247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8823f10e09d28d63d87941099ddb621e.png)
(1)求该函数的定义域;
(2)判断该函数的奇偶性;
(3)探究该函数的单调性及最小正周期,并求其值域.
您最近一年使用:0次
5 . 下列函数中,同时满足:①在(0,
)上是增函数:②为奇函数:③周期为π的函数有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
A. ![]() | B.![]() |
C.![]() | D. ![]() |
您最近一年使用:0次
解题方法
6 . 下列函数为偶函数的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知函数
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938d750b351ade857743de90798396cd.png)
,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a843bcffc7682b593187dac0604ae55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938d750b351ade857743de90798396cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef9d3d0789849bce36e6ed8c08a50cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a989c4fbf0ff34cedb365d2dda47f16.png)
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8 . 定义行列式运算法则为:
,已知函数
.
(1)求
的最小正周期;
(2)若函数
是偶函数,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e02900952635dbc28821f3e2f84ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b77c5506f9e91f078a7e318c99231e0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7bc838f91dff6957b471077dab7bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2c01ac2a7f6ad7e03cb7a61daefab.png)
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9 . 已知函数
.①
的最小正周期为
;②
是奇函数;③
的一个对称中心为
;④
的最大值为
,最小值为
.上述说法正确的是__________ .(填序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf73988aa4d9961565ff07d136c13b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b3a91ccf6028608cd03df7072f6536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1113c6332e31f6642a73fc91ec34723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
您最近一年使用:0次
2019-12-13更新
|
374次组卷
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2卷引用:贵州省毕节市实验高级中学2018-2019学年高一上学期期末数学试题