解题方法
1 . 记不等式
(其中常数b为正实数)的解集为A,不等式
(其中k为常数)的解集为B,并设集合
.
(1)当
时,求集合A;
(2)试根据正数b的不同取值,讨论是否存在实数k,使得
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66efe401ad64c1b68422ccdb72d73c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45462950bdacda081bb801b0cc9df1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c47a941600c5eb365e0fd6f74dec78e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
(2)试根据正数b的不同取值,讨论是否存在实数k,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22882310035db6d3d953e060b0c91733.png)
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解题方法
2 . 求范围和图象:
(1)
的函数图象先向左平移
个单位, 然后横坐标变为原来的
,得到
的图象,求
在
上的取值范围.
(2)如图所示, 请用“五点法”列表,并画出函数
一个周期的图象.
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/69418aa885c148baad8dd40f0ed7084e.png?resizew=297)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f457df0f9d14437a7f0443bb297e6ee8.png)
(2)如图所示, 请用“五点法”列表,并画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c3d302e263382a01339fa43fece182.png)
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/69418aa885c148baad8dd40f0ed7084e.png?resizew=297)
![](https://img.xkw.com/dksih/QBM/2022/3/14/2927732832747520/2937564027559936/STEM/c7574a95-f8a7-44e7-a7fd-3fb3a5f67026.png?resizew=376)
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2022-03-16更新
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758次组卷
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3卷引用:浙江省杭州第二中学2021-2022学年高一上学期期中数学试题
名校
解题方法
3 . 已知函数
在
上有意义,且对任意
满足
.
(1)求
的值,判断
的奇偶性并证明你的结论;
(2)若
时,
,判断
在
的单调性,并说明理由.
(3)在(2)的条件下,请在以下两个问题中任选一个 作答:(如果两问都做,按①得分计入总分)
①若
,请问是否存在实数
,使得
恒成立,若存在,给出实数
的一个取值;若不存在,请说明理由.
②记
表示
两数中的较大值,若对于任意
,
,求实数
的取值范围?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c275d203295b989c129101d82e74ae01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f97718f1472e11502eaa775b58bd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608fd0dfd30079f4337ef571571eb287.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afeede1e920a57feb40fc0cd66b961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7baa4f3372e6a0aa38056e0de3b0fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6000b174147cec2de26041837aec1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c275d203295b989c129101d82e74ae01.png)
(3)在(2)的条件下,请在以下两个问题中
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad3411b2f63b59dafb6fccdacddd1fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32f78e3f288a433f8ba3661e551af4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eabe40ebe23d91aa1447b9896b300f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287376282d8c04d267ec6add486853f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd851ca08ce2b6224e9d5e9952cff60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2021-12-12更新
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917次组卷
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2卷引用:北京师范大学附属中学2021-2022学年高一上学期期中考试数学试题
21-22高三上·北京·期中
名校
4 . 已知函数
.
(1)求
的单调递增区间;
(2)若
在区间
上的最大值是
,求
的取值范围;
(3)令
,如果曲线
与直线
相邻两个交点间的距离为
,求
的所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f734c7bab5a46c252054c0c7c58c1c38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb37d173605f006df4c51ba63b1841d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2665cce8924f0d96c37e25ffdc982d7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d74c0570f3ef4fff3e0ba34204f8d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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解题方法
5 . 条件①:
;条件②:不等式
的解集为
.已知二次函数
满足
,再从条件①和条件②两个条件中选择一个作为已知.(注:如果选择条件①和条件②分别解答,按第一个解答计分)
(1)求
的解析式;
(2)若函数
的图像总在一次函数
图像的上方,试确定实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c292ad5ab432ba87d945d952ae84d2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351e06f62c94dfde21e0689d7bf35ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881fe2df23c5a0fe1d1fecbe9ffa55fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.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/12f9bd7fdb0c44b5e2e1d5a59dd6f7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
6 . 已知函数
(
且
),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc3bdec262e05c4b4c3bb0740af8842.png)
(1)求不等式
的解集.
(2)若函数
过点
,并且函数
满足
,求实数a与k的值.
(3)在(2)的条件下,判断函数
在
上的单调性(不必说明理由).若
时,不等式
任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba45e9db08ea78bad8b87c6e67b55b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74110bc818c2f5a53d63451c5251eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9933657444761c72ceb4b0c9017578a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc3bdec262e05c4b4c3bb0740af8842.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68225d7ad08d86a5a634eb2e6b83542.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010c74de86f432499fe7246a199721ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b588232e4a4af8221768af9e332b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5272fd043d44affb650f15b4d5c934b3.png)
(3)在(2)的条件下,判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d913b3ffc1962e2c255e6ea4c4fd0fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3970809a652cf8ad7b619aaaed353f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c631bc5567447afcb4e4a19dfae6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26497bc1d93c4679b629bc909038d595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
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2022-10-24更新
|
351次组卷
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2卷引用:天津市四校(杨柳青一中、咸水沽一中 、四十七中,一百中学)2020-2021学年高一上学期期末联考数学试题
名校
7 . 已知关于
的不等式
.
(1)当
时,求上述不等式的解集;
(2)若上述不等式的解集为
,求不等式
的解集;
(3)若上述不等式的解集为
,求
的取值范围;
(4)结合此题填入部分数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6d03dfc5b4ce38e17403b3b49fdc15.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
(2)若上述不等式的解集为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee5d0f947429f7dc4572cd4cf46c5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51540993df966940e00eea51cd57073f.png)
(3)若上述不等式的解集为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(4)结合此题填入部分数据
![]() | 不等式![]() |
![]() | |
![]() ![]() | |
![]() |
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解题方法
8 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f294ed9d641d73656256d524359d3d42.png)
![](https://img.xkw.com/dksih/QBM/2021/12/15/2872923657486336/2880700403081216/STEM/b0a0bba53d9b4a7298923811c17db260.png?resizew=303)
(1)请在下面坐标系中画出函数
的图像.
(2)不等式
的解集为________.(写出结果即可,不需写过程)
(3)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f294ed9d641d73656256d524359d3d42.png)
![](https://img.xkw.com/dksih/QBM/2021/12/15/2872923657486336/2880700403081216/STEM/b0a0bba53d9b4a7298923811c17db260.png?resizew=303)
(1)请在下面坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbf4962baeb259c03bceb50d12674f9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d2dda7ff193c06887f56554ab9aae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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2021-12-26更新
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2卷引用:辽宁省六校协作体2021-2022学年高一上学期第三次考试数学试题
名校
解题方法
9 . (1)命题
,
成立,若命题
为真命题,求
的取值范围;
(2)讨论关于
不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d74f393239d0dec64af568adefdb8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10556c893b82b0f97a205d9e520fc907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)讨论关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79572b2647d73017e8139cc5eabd8f11.png)
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2021-11-08更新
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3卷引用:辽宁省沈阳市第二十中学2021-2022学年高一上学期10月月考试数学试题
辽宁省沈阳市第二十中学2021-2022学年高一上学期10月月考试数学试题陕西省宝鸡市陈仓区2022届高三上学期第一次教学质量检测文科数学试题(已下线)专题29 不等式选讲解答题20题-备战2022年高考数学冲刺横向强化精练精讲
名校
10 . 设二次函数
.
(1)若
,
且二次函数的最大值为正数,求
的取值范围.
(2)若
的解集是
,求
的解集.
(3)设二次函数
的两个零点分别为
,
,满足
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352b2e643a7ce605334f1b0e572bfb0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566bfdd14f1aa396f620e0ca6895a21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f3d2d9f66307b7af2398efdb893bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa220ab7c91ffa40202bcc544aa2bb2.png)
(3)设二次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd69aebdafb31468eb13ce3b28a36e47.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/57cfda1c04b6eaeb5e78018539c2880e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37902f139fee3d5a5ac74b21b0a0e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1ad9f639b70bf98fe33ca163a8922f.png)
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