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
名校
2 . 已知函数,则下列说法正确的是( )
A.![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若方程![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知函数
及其导函数
的图象如下图所示,若函数
在
上恰有3个不同的零点
,
,
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4250e1272028150feeab816d9fec43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5175a4148b2a704eb29dd3bb77d033c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e615a5ca4d8e679a19c4e90687c59d66.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/35bacde908aec2c313978fc4309d82bc.png)
您最近一年使用:0次
名校
4 . 已知函数
的图象的两相邻对称轴之间的距离为
,且在
时取得最大值2.
(1)求函数
的解析式;
(2)当
时,若方程
恰有三个根,分别记为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df94a45a83636c4603aeae49eb44473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de633b2c143b9f76b29cde1c6ffce71.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d6804ac95bb944d0fa77c6f2813e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bacde908aec2c313978fc4309d82bc.png)
您最近一年使用:0次
2024-02-25更新
|
737次组卷
|
2卷引用:1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(理科)试题(六)
5 . 已知函数
满足:
.若函数
在区间
上单调,且
,则当
取得最小值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2368152802235d8226a27d3910784811.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c89e928883251360546be8f2a739e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a847a2afdc2f6821fa267fe7d9e5c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351629c193354cdcf202133052e45028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1540b6b10f07a867618a1eec02e2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c823b1db20dcf7e5272b9b2f548c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2368152802235d8226a27d3910784811.png)
您最近一年使用:0次
名校
6 . 已知函数
在区间
上有且仅有4个极值点,给出下列四个结论:
①
在区间
上有且仅有3个不同的零点;②
的最小正周期可能是
;
③
的取值范围是
;④
在区间
上单调递增.
其中正确结论的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8489d68c0db0ed5cfd15986cc8edf723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4b61d912f99e5583e7e17cf8fef558.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23efa380a58dc9663ba06dc249ce721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bbecff2a997cd7d682e20986259685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cb8341e1e034580e40fb36c69c7042.png)
其中正确结论的个数为( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2024-01-13更新
|
776次组卷
|
4卷引用:2024届陕西省渭南市高三一模数学(理)试题
2024届陕西省渭南市高三一模数学(理)试题(已下线)专题05 三角函数4-2024年高一数学寒假作业单元合订本四川省成都市石室中学2023-2024学年高一下学期开学考试数学(理科)试卷四川省成都市石室中学2023-2024学年高一下学期开学考试数学(文科)试卷
7 . 已知点
在函数
的图象上,点
在函数
的图象上,且
,
,
,给出下列说法:
①当
时,
;
②存在点
在直线
上;
③
,
,使点
和点
为两个函数图象的公共点;
④若点
在函数
的图象上,则函数
的周期是
,
两点间距离的整数倍;
⑤定义满足长度
取最小值时的区间
为最小区间.若
,区间
是满足
的最大区间,则函数
的周期为
.
其中,说法正确的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369e2cc0b7c553969627461819e80229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04129b7390acd7d936fbd204cc111dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7602e4015d02cb188ffb82092ee980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d62cdf358f79c7831dd009c26430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b519531dbeee800a08ba5ce55ff7e51.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d387a4f4ed6f48afd7fc75ff68ae026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75ff0c325ddcac48cf1c233f033c2c7.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67de794bd1d73ebe1e7fca6622579587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677ad4c4ea0722f0ee064f44624c585f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d62cdf358f79c7831dd009c26430c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369e2cc0b7c553969627461819e80229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
④若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6db7130ea4b0ea4da3d316b3070f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e59bc063c88b1add34184da82283251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e59bc063c88b1add34184da82283251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
⑤定义满足长度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31d1c786e88987bb3bc7c54b7b66819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85cbdee531d4b394d674d90adda132b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b83fe99c90a7bf139a7e6e537820c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00feb80debaf63029240652a21b4b38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04129b7390acd7d936fbd204cc111dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
其中,说法正确的序号是
您最近一年使用:0次
名校
解题方法
8 . 若函数
满足:对任意
,则称
为“
函数”.
(1)判断
是不是
函数(直接写出结论);
(2)已在函数
是
函数,且当
时,
.求
在
的解析式;
(3)在(2)的条件下,
时,关于
的方程
(
为常数)有解,求该方程所有解的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8a845744f91c1ca0772a60989415c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1fe3f8c0ddaa9a5291f049ecc873da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)已在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc5e806b6f4d556bbd8039c6936e773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bf9a635dd1cea0cd6f0495c292f1f7.png)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505a8a32e68077195084c51eb5b03c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-12-19更新
|
457次组卷
|
2卷引用:浙江省杭州学军中学(紫金港校区)2023-2024学年高一上学期12月月考数学试题
9 . 已知函数
在
上是增函数,且
,则
的取值的集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259e60b394dcef598d079377a86057f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24505fae9d665ae10fca1d7408b91ed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1180f0fc466a4b1056d801e55edb93e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66831c9c25d51b1c27b3f1ff411d962f.png)
您最近一年使用:0次
10 . 已知函数
在
上是增函数,且
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ccfdd389279f17fb22ba542c045114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a325856063c83c6df7b478255c8901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43fc8b890adf3d7c394159cfa90b00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次