名校
解题方法
1 . 已知二次函数
满足
.
(1)求
,
的值;
(2)求证:
的图像关于直线
对称;
(3)用单调性定义证明:函数
在区间
上是增函数;
(4)若函数
是奇函数,当
时,
.
(i)直接写出
的单调递减区间为_________;
(ii)求出
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab93efd42a3054040ccff8adf697c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3749d9ddfb2908ac0ee444743fe72afd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
(3)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/189b2da6c420bf8f8900002d14f65f72.png)
(4)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1a94ea3c278c2197572cc1b7725b1.png)
(i)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(ii)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
解题方法
2 . 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
3 . 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
|
588次组卷
|
3卷引用:北京师范大学附属实验中学2021-2022学年高一下学期“线上擂台赛”数学试题
解题方法
4 . 已知定义在R上的函数
,
(1)求证:
是
图象关于直线
对称的充要条件;
(2)若函数
满足
,且在
单调递增,求解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1576c2056a224c7e4ea25f73963979e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/935799b8d9f3de0c021e2a7df70d96f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b50afbb876722239c68f8f4487d77f.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
(1)求证:函数
是
上的减函数;
(2)已知函数
的图象存在对称中心
的充要条件是
的图象关于原点中心对称,判断函数
的图象是否存在对称中心,若存在,求出该对称中心的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1bc9a5703351bea65b904292db4e01.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c86212cfe7338ae7adca7d58eca15fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
解题方法
6 . 已知定义域为R的奇函数
最大值为2,在
上单调递增,在
单调递减,且当
时
,
(1)求函数
在
的单调性并证明;
(2)求函数
的最小值,并说明理由;
(3)直接写出函数
图象的对称中心坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55de1c1936c51ce70e19f6989ba68dc6.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)若
,求证:函数
的图象关于点
中心对称;
(2)若
,且关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8df2dd829c8d0b369e6ce0752f96fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefeac0d38a1a529666ebbb9278835a2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda3fef556938fce034a3a7a706fc71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-11-14更新
|
820次组卷
|
3卷引用:安徽A10联盟2021级高二上学期开学摸底数学试题(北师大版)
解题方法
8 . 已知函数
.
(1)求不等式
的解集;
(2)若关于
的方程
在
上有解,求实数
的最大值;
(3)证明:函数
关于点
中心对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77735219de6cba682378dee5712988c.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a4dd6a73d0d00678668143fa1ed2a8.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31bc0c34811edba74dae3fcaed8f577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe8803bc5d850ec2a6f15bcdb12c896.png)
您最近一年使用:0次
解题方法
9 . 我们知道,函数
的图象关于坐标原点成中心对称图形的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.
(1)求函数
图象的对称中心;
(2)若(1)中的函数
与
的图象有4个公共点
,求
的值;
(3)类比题目中的结论,写出:函数
的图象关于直线
成轴对称图形的充要条件(写出结论即可,不需要证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830a9e13de1222eb9c3d5e4b636f50fa.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789c5a8a2fb3b6c4951b762aab04606.png)
(2)若(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6e4e1f96f85068816343f9f142616a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae243b023bd610457e6dc8ab00746fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89739c60fe1a969349ea408f1bf0c7fc.png)
(3)类比题目中的结论,写出:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
您最近一年使用:0次
2023-02-19更新
|
432次组卷
|
7卷引用:四川省巴中市2022-2023学年高一上学期期末考试数学试题
解题方法
10 . 已知函数
的定义域为集合
,且
.
(1)求
,
的值;
(2)判断
在
上的单调性,并用定义证明;
(3)若
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1d9118acff9cf8eb508a03109eca76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf6f9f3cd574d60f3baecb9b10af53e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543945660885cd4c9ff3979e9358950e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a85efec16cd028b046aa586f59cbc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed7959ecf48b8aed3ce7d672bd1b773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2022-12-10更新
|
213次组卷
|
3卷引用:福建省永泰县城关中学2022-2023学年高一上学期期中考试数学试题