1 . 已知函数
,在曲线
与直线
的交点中,若相邻交点的距离为
.
(1)求函数
的解析式;
(2)若
,解不等式
;
(3)若
,且关于
的方程
有三个不等的实根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479e46aee3431e9206aed77d82caf96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f36632a97ab742ce7d12bd3fd6ab00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b34d7db59e5fc4abeb3589ed4ebe56a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f36632a97ab742ce7d12bd3fd6ab00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e44327127832b6bfbfce22b9c65f5fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知函数
的部分图像如图所示:
的表达式;
(2)当
时,求方程
的所有根的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36c65ad4f3d66beaf187cec1bb201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefa56d3b14ddc6ce99262bb90de45ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a388e651e4e125fbed261b773c6d1e.png)
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名校
3 . 在条件①对任意的
,都有
;条件②
最小正周期为
;条件③
在
上为增函数,这三个条件中选择两个,补充在下面的题目中,并解答.
已知
,若______,则
唯一确定.
(1)求
的解析式;
(2)设函数
,对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4becec171b43ff11b58285a7cf5fd6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e8a607883e46aa52f2cad51a5ddacff.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b0df153aacb820a9109d4651413d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69b5b8c4c24eab782174c5cae1b88a5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca82b2d1d8da50fd128c4a9766203406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9720087e589bf3d16877ddcf4712cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da74439c435a5419800b670203d6d719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-05-29更新
|
393次组卷
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2卷引用:北京市首都师范大学附属中学2023-2024学年高一下学期4月期中考试数学试题
名校
4 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e658113eadee1b45111b2a927c24e2f.png)
(1)某同学用“五点法”画出函数
在某一周期内的图像,列表如下:
请填写表中的空格,并写出函数
的表达式
(2)若
,将函数
的图像向右平移
个单位长度,再向下平移10个单位长度后得到函数
的图像,求函数
的零点所组成的集合;
(3)对于(2)中的函数
,证明:存在无穷多个互不相等的正整数
,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e658113eadee1b45111b2a927c24e2f.png)
(1)某同学用“五点法”画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![]() | ![]() | ![]() | ![]() | ||
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | ![]() | 0 | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3b825b865672c849f8bc7d45e6244e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)对于(2)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21bbc2539e1b3815242c95118e9b0784.png)
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5 . 已知函数
的部分图象如图所示.
的解析式.
(2)当
时,关于
的方程
有两个不同的实根
,且
.
①求
的取值范围;
②求函数
的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0f153e044199055eec43c5226c5241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd65d7c5e979706d391163aee2c18cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed07a76ec8ea66b7fdb8088098ca9ec.png)
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2024-04-26更新
|
272次组卷
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3卷引用:江西省部分学校2023-2024学年高一下学期4月期中考试数学试题
江西省部分学校2023-2024学年高一下学期4月期中考试数学试题(已下线)高一下期末考前押题卷02-期末考点大串讲(人教B版2019)河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期6月月考数学试题
名校
解题方法
6 . 已知函数
的图象关于直线
对称.其最小正周期与函数
相同.
(1)求
的对称中心,
(2)若函数
在
上恰有8个零点,求
的最小值;
(3)设函数
,证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afb9095c987bf16ce83bd1d4e77427c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24db7b603aebdee8e298d1fe49c848e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcac0f78f7633458b355150c8d477f2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a39725e447560a9dd575264182bd6ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec509982a9ba36e2d8a2c3e5419acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0d6508c370089860a78c8079405681.png)
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名校
7 . 已知函数
的部分图象如图所示.
的解析式;
(2)已知
,求
的值;
(3)若关于
的方程
在
上有两个不同的实根
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c5e2d6ede6688e018fc37726278ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2620409ffb73c21bd3261de324a0fb0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccdd875fa5f0b379c144b9a979e535b.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da3023b0765cfb1b268e29e1d01de0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45363c988b76c3b33a79cd60b99ba8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e522c7f5814c715334b01c532ef6de8a.png)
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2024-03-21更新
|
494次组卷
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2卷引用:湖南省多校联考2023-2024学年高一下学期入学考试数学试题
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解题方法
8 . 某医院发热门诊改造,如图,原发热门诊是区域
,可利用部分为扇形区域
,
,
米,
米,区域
为三角形,区域
为以
为半径的扇形,且
.
外轮廓设置隔离带,求隔离带的总长度;
(2)在区域
中,设置矩形区域
作为便民门诊,求便民门诊面积
最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0947161887af7b78afde80c0cd647d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d276b69c758da6bf9e2fb7f63130bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab51246d895d2a255f3314c853000ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca634fc3392fe8983b44acfb86f835a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c83b688911f105cffe00d6d54eea13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cbbac19ce207b72c990195854f6fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
(2)在区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d276b69c758da6bf9e2fb7f63130bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e5c1767a5719a03062ebb0fc5067b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2024-03-12更新
|
281次组卷
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3卷引用:黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷
黑龙江省哈尔滨师范大学附属中学2023-2024学年高一下学期开学考试数学试卷上海市川沙中学2023-2024学年高一下学期期中考试数学试题(已下线)专题01 三角-期末考点大串讲(沪教版2020必修二)
9 . 已知函数
,相邻两对称轴之间的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
的值;
(2)若
时,方程
有解,讨论方程解的个数,若方程所有解的和记为
,求
所有可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f43285a39fa2bf73a37c9efdc80a989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd29544a6b056940d248c2fa4ec36043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c35393080972a7620f980c4f37d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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解题方法
10 . 已知函数
和
的定义域都是
.
(1)请在同一平面直角坐标系上画出函数
和
的图象;(不要求写作法)
(2)求两图象交点的横坐标,并解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5dd64c0871cc50aaf3e83f20c12f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceba1ae12f82ba120e9be574e24e77b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f96a23757dc485b91a6b78b496922b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/45f22448-4104-413d-b512-c950362c1910.png?resizew=210)
(1)请在同一平面直角坐标系上画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)求两图象交点的横坐标,并解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1102dbf92bc3eb1cd913fab5c914d703.png)
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