名校
解题方法
1 . 某城市为了鼓励居民节约用水,采用分段计费的方法计算用户的水费.计费方法如下表:
(1)设每户每月用水量为x
时,应交纳水费y元,写出y关于x的函数关系式;
(2)若某同学家本月交纳的水费为60元,则其本月用水量是多少?
每户每月用水量 | 水价 |
不超过12![]() | 3元/![]() |
超过12![]() ![]() | 6元/![]() |
超过18![]() | 9元/![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eab9bcb68861b73f12a65eb9e94700d.png)
(2)若某同学家本月交纳的水费为60元,则其本月用水量是多少?
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2 . 已知函数
.
(1)求
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd0542daea7e21e4127b39b412f1e1f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c871677f7b3fdc2c399a8b8de86b57f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e9089e21e10f127e970d8e42e55244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
3 . 已知函数
,其中
,
.
(1)求函数
的解析式;
(2)已知方程
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a6051edd6051e277a17741867bc425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c131afe88023786e754e43689628c67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a0169e37472db54391a8d175f8b2de.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
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名校
解题方法
4 . 黎曼函数是一个特殊的函数,是德国著名数学家波恩哈德·黎曼发现并提出,在数学中有广泛的应用.黎曼函数定义在
上,
.
(1)请用描述法写出满足方程
的解集;(直接写出答案即可)
(2)解不等式
;
(3)探究是否存在非零实数
,使得
为偶函数?若存在,求k,b应满足的条件;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8e2adb558703f59612bc01f2fb6b5.png)
(1)请用描述法写出满足方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136acbcd8cebcc7153a67f329630b6af.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fead3304932a65d71f88d5002bea5b2b.png)
(3)探究是否存在非零实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceee0ff5c929d67de3c294e027c9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957bd952797bcd94260595386ca07732.png)
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名校
5 . 已知函数
.
(1)当
,且
时,求
的值;
(2)若存在区间
(
为函数定义域),使
在区间
上的值域也为
,则称
为
上的精彩函数,
为函数
的精彩区间.求
是否存在精彩区间?如不存在,说明理由;
(3)若存在实数
使得函数
的定义域为
时,值域为
,则称区间
为
的一个“罗尔”区间.已知函数
存在“罗尔”区间,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370efb70486b9964df67552cb7734ec5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7266b2ef457b8ddeee3fa2cc24022e.png)
(2)若存在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9dbaef457ca0cad2815d03a17e5d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030052a6936e5136de625c65eea375af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
6 . 已知函数
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
(1)若
,
,求实数
的值;
(2)若函数
的值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbc52b0a7bb63234a705dd3d5ae9e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a2b3d797aa62f036c4f6172d38c858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
7 . 已知函数
.
(1)若
时,求
的值;
(2)若
时,且
,求
的值;
(3)若
在R上是增函数,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3e383174b251a0a6110702b27c6446.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499109aa338f9c5da30ae0a590809f3b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知函数
.
(1)求
,
的值;
(2)若
,求实数a的值;
(3)直接写出
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e59472cb37535373406936547242dc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef42da484f79cfaa474a289343cc8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754386f1d84e582d52d8219080a81528.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8935dc56111774227294e35d34c6200f.png)
(3)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac26961bab48a9301f307274649e4981.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/2898253d-4de8-44c0-a716-1407a4e58e6f.png?resizew=213)
(1)求
的值;
(2)若
,求
的值;
(3)请在给定的坐标系中画出此函数的图象(画到答题卡上的坐标系中),并根据图象写出函数
的值域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac26961bab48a9301f307274649e4981.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/2898253d-4de8-44c0-a716-1407a4e58e6f.png?resizew=213)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4474bd87c00ac3ee99ab366527ded109.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04042cd29185f7f48399495d7df371e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)请在给定的坐标系中画出此函数的图象(画到答题卡上的坐标系中),并根据图象写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
10 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/7c47aec2-8781-4f6d-8228-392de212f77c.png?resizew=141)
(1)已知
,求a的值;
(2)作出函数的简图;
(3)由简图指出函数的值域;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598ff8437bad090879fc7ee84ea37b29.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/7c47aec2-8781-4f6d-8228-392de212f77c.png?resizew=141)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7a129587e063a30e6d6449637f2b19.png)
(2)作出函数的简图;
(3)由简图指出函数的值域;
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