名校
1 . “函数
图像关于原点对称”的充要条件是“函数
对定义域内的任意
都满足
”.
(1)若定义在
上的函数
图像关于原点对称,且当
时,
,求函数
的解析式;
(2)类比上述结论,得到以下真命题:“函数
图像关于点
对称”的充要条件是“函数
对定义域内的任意
都满足
”.若函数
的图像关于
对称,且当
时,
,
(i)证明:函数
在
上单调递增;
(ii)关于
的方程
在
上有四个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc1ba1c08611beeea6aef9db37a821b.png)
(1)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)类比上述结论,得到以下真命题:“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d8a34a28f2c13ea40d7ae90c752005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f4ce3e8739236c298b9c944a296ab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ec21e660222f593dc2ec2175dd03e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd44d8368c2f4877ec8aa9683373ad0.png)
(i)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b645d3b2f4193f7cbee1ceedd8fc8f7.png)
(ii)关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b692232539a5e43872db9c9c32e9d301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818ffdea5243b82d9892012b0099f4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
2 . 设
是定义在
上的奇函数,且对任意
,都有
,当
时,
.
(1)当
时,求
的解析式;
(2)设向量
,
,若
,
同向,求
的值;
(3)若
,
,
,若不等式
有解,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6badf1414c66f33f264d2fd5ca43f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2222b10f3189590dfa35385970ce40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715257c83da5d36ce96caf93244356ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5ffe326b3630c0b860f26597dcccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca718d154417114e49d866bba4c48be.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0345b571f7e0adba412a1899256651e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869d17dff6b5a72789930157ee142655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323dc838fc738bfb6a0720413efdbef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
为
上的偶函数,当
时,
,对于结论
(1)当
时,
;
(2)方程
根的个数可以为
;
(3)若函数
在区间
上恒为正,则实数
的范围是
;
(4)若
,关于
的方程
有
个不同的实根.
说法正确的序号是___ .
![](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/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce427e97019745d570dd2728027fba5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0748eafe2c69f995fdb032b8afc127.png)
(2)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4724381345ed23396777a9be9466a78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68361a0dd9b8debcc9d19558184a5c5.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f2d98207e6688e7233bb22d5908ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfdd3d02b54e997cbec983d80f6bafd.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ee5f43412795671704ab0e8d0b2f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b393334bedc719f3474f5afc867042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
说法正确的序号是
您最近一年使用:0次
名校
解题方法
4 . 已知偶函数
,奇函数
,若满足
.
(1)当
时,求函数
的最小值;
(2)当
时,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f042c703ec60e843927a18a4384324f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec0e56a0e05cf5605e0642a842b6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1736c2110d492999b57af05062e62151.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad05719025457903d1b5d5c7b99f97f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff3b548f6c0c5cf72d212ae46914bc8.png)
您最近一年使用:0次
5 . 下列说法正确的是( )
A.若函数![]() ![]() |
B.函数![]() ![]() |
C.若函数![]() ![]() ![]() ![]() ![]() |
D.若函数![]() ![]() ![]() |
您最近一年使用:0次
名校
6 . 已知偶函数
满足:
,且当0≤x≤2时,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8127a4b0b81fdeefcfb9bdc2c7dd05d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a2532f0f9197e40db2e76c3dfc9301.png)
A.-2≤x≤0时,![]() |
B.点(1,0)是f(x)图象的一个对称中心 |
C.f(x)在区间[-10,10]上有10个零点 |
D.对任意![]() ![]() |
您最近一年使用:0次
2021-05-26更新
|
1847次组卷
|
6卷引用:浙江省杭州市长河高级中学2022-2023学年高一上学期期中数学试题
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