名校
1 . 已知函数
,关于
的方程
有以下结论:
①当
时,方程
恒有根;
②当
时,方程
在
内最多有9个不等实根;
③当
时,方程
在
内有两个不等实根;
④若方程
在
内根的个数为正偶数,则所有根之和为
.
其中正确的结论是_________ (填写所有正确结论的编号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/286cd9209dcde634611ccaa9889c9946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8feacf2a03d30273886b8217e7a5d7a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8feacf2a03d30273886b8217e7a5d7a.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8feacf2a03d30273886b8217e7a5d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d72d992e234cd12b425c22a488c50c4.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4d0aca3657c6d99e820e2567f18683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8feacf2a03d30273886b8217e7a5d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce045db1b01f66f7db3070eb06d4e6a.png)
④若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8feacf2a03d30273886b8217e7a5d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d72d992e234cd12b425c22a488c50c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a451c09c095823a0ff113bdd583bb33.png)
其中正确的结论是
您最近一年使用:0次
2 . 已知函数
若方程
有且只有五个根,分别为
,
,
,
,
(设
),则下列命题正确的是_____________ (填写所有正确命题的序号).
①
;②存在k使得
,
,
,
,
成等差数列;
③当
时,
;④当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a696b23bf6556ef55eeeff5379080ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48dc6d0827a159050e3fa55164f258b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9b42973c53907f09f2de384c42fc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acd5e05f89802149b8b810c24d6ac73.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b59d678b4c4aa0ec2bb04be1b2739a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9b42973c53907f09f2de384c42fc5f.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779bc714193033c738599c30487bd42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c12f6211f669ab04f4fe1c1b279ac2e.png)
您最近一年使用:0次
解题方法
3 . 已知函数
,关于
的方程
有以下结论:
①当
时,方程
恒有根;
②当
时,方程
在
内有两个不等实根;
③当
时,方程
在
内最多有
个不等实根;
④若方程
在
内根的个数为正偶数,则所有根之和为
.
其中正确的结论是__________ (填写所有正确结论的番号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1152dac89a5550489f036c7c59fc72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c5a01371237d9f145c03922f313fc8.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c5a01371237d9f145c03922f313fc8.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4d0aca3657c6d99e820e2567f18683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c5a01371237d9f145c03922f313fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c5a01371237d9f145c03922f313fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1007ff46f40af735a749d6650646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
④若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c5a01371237d9f145c03922f313fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267e1007ff46f40af735a749d6650646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d93ea6b78c16307d56cba63315d0051.png)
其中正确的结论是
您最近一年使用:0次
解题方法
4 . 函数
是周期为2的周期函数,且
,
.
(1)画出函数
在区间
上的图象,并求其单调区间、零点、最大值、最小值;
(2)求
的值;
(3)求
在区间
上的解析式,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4faa700e1f7bfcd87147706cead7b858.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7deb5250a15a93a4b116d19c43a4d99f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf910f82c3094b267a3d481d23d829f.png)
您最近一年使用:0次
名校
5 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/5eedc2cc-bfff-4d1b-b3a4-ff8e8cfd4c15.png?resizew=171)
(1)用分段函数的形式表示函数
的解析式,并画出
在
上的大致图像;
(2)若关于x的方程
恰有一个实数解,求出实数m的取值范围组成的集合;
(3)当
时,求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7247a12f18390a9f9a997cc87ed6fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/5eedc2cc-bfff-4d1b-b3a4-ff8e8cfd4c15.png?resizew=171)
(1)用分段函数的形式表示函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ff4a1f5d3ad9d7668fe555e70b774c.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31bc0c34811edba74dae3fcaed8f577.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874dcc6d4f0abe55891d240b90c5d6bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次