解题方法
1 . 设函数
.
(1)若对任意实数
,
有
成立,且当
时,
;
①判断函数的增减性,并证明;
②解不等式:
;
(2)证明:“
图象关于直线
对称”的充要条件是“任意给定的
,
”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe10ebb50c9dfcf2570083b9321d281.png)
(1)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e36e45821cc161584ad64043772227a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
①判断函数的增减性,并证明;
②解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67748e1777567c2f05835fe6fe6f5303.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe10ebb50c9dfcf2570083b9321d281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3dbcdab81b677ce015ee99f0445864.png)
您最近一年使用:0次
名校
解题方法
2 . ①函数值域为
;②函数为偶函数;③函数在
上
恒成立;④若任意
都有
.已知函数:①
;②
;③
;④
.其中同时满足以上四个条件的函数有( )个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698cf53f76a1d637dfe2732d0a866eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce3f649aab0a3b77c09d935817247db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a7901661c71b40b5601ad0c0f6dacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5968769e7df85d95f50ed61defe2ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b10c58557ed77f3524187c91d55bf76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbc6010bbc3c5229b69a96746028839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dd4e188adaccfbbd66942c2ff80d35.png)
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)求证:函数
是
上的减函数;
(2)已知函数
的图像存在对称中心
的充要条件是
的图像关于原点中心对称,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/4077e55784510b6adc6a040daa85eb18.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c86212cfe7338ae7adca7d58eca15fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3ed9c4fa3bce5d45202695bbc179d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55e9f87ebd16be23db0e9fea26da11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e9fc70929247a1cdc2e8fc5c83df2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-12-20更新
|
727次组卷
|
4卷引用:第5章 函数的概念、性质及应用(B卷·能力提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(沪教版2020必修第一册)
名校
4 . 已知函数
的定义域为
,值域为
,下列关于函数
的说法:
①、当
时,
;②、将
的图像补上点
,得到的图像必定是一条连续的曲线;
③、
是
上的单调函数;④、
的图像与坐标轴只有一个交点.
其中正确命题的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68dc561eb1029c7c9b778484974df0eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07acbdd73fb4189184ccffd4e6a080a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
①、当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7666ed2a5d6e02fe4690594751ef79.png)
③、
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6519c2b271eca4dca6b6f66df899462f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
其中正确命题的个数为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
5 . 若两个函数
和
对任意
都有
,则称函数
和
在上
是疏远的.
(1)已知命题“函数
和
在
上是疏远的”,试判断该命题的真假.若该命题为真命题,请予以证明;若为假命题,请举反例;
(2)若函数
和
在
上是疏远的,求实数
的取值范围;
(3)已知常数
,若函数
与
在
上是疏远的,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68dcefc64522affe52cb23609e1ed318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64537743379242ee87505563d3a92ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df606d4adb89b5473944bb98363a6f53.png)
(1)已知命题“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b6e13798211ab7a313b83bb958a009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5013206591edea029e8748159034a308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69825660f852b3e07e21ddd804c4afb.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b6e13798211ab7a313b83bb958a009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5013206591edea029e8748159034a308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d090c9fd3be22879e33f58e23be1bc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4cc00c283519973f7f8e1274b5c733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944d9ff34a45741697f2e5c115af1074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30334e741241937414a7c09ba4759989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c70eceeee00d6fcc82d35d24618dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
2021-09-15更新
|
861次组卷
|
4卷引用:上海市金山区2020-2021学年高一上学期期末数学试题