解题方法
1 . 设
,
(1)在所给直角坐标系中画出
的图象;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/29/1ca98915-0238-4116-a7dd-7a2d37e3ec24.png?resizew=294)
(2)若
,求
的值;
(3)若
有三个根,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844f6833faa3a5f8aef195727b77e4da.png)
(1)在所给直角坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/29/1ca98915-0238-4116-a7dd-7a2d37e3ec24.png?resizew=294)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e1a4f3d0f4f608ea4e8481843d19429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知函数
.
(
)画出函数图象.
(
)写出函数
的单调区间和值域.
(
)当
取何值时,方程
有两不等实根?只有一个实根?无实根?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec29d3d5f086a6802cfd748c2d7089c.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342d52fc26cc550a45b80756903bee6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/c9fb2ff4-c600-42de-9f16-c4077f3dfdbb.png?resizew=207)
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3 . 已知函数
的分段形式为
.
![](https://img.xkw.com/dksih/QBM/2020/12/21/2618873736929280/2620210443231232/STEM/56055d9390aa4797b8e0a7412a4f2c42.png?resizew=261)
(1)作出函数
的图象;
(2)若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ee0f31ceb625bf12f0fab3cf26c7b6.png)
![](https://img.xkw.com/dksih/QBM/2020/12/21/2618873736929280/2620210443231232/STEM/56055d9390aa4797b8e0a7412a4f2c42.png?resizew=261)
(1)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be65233277643e084c5b6a8651956e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 我国是水资源匮乏国家,节约用水是每个中国公民应有的意识.为了保护水资源,提倡节约用水,某城市对居民生活用水实行“阶梯水价”,计费方法如下表:
(1)该城市居民小张家月用水量记为
,应交纳水费y(元),试建立y与x的函数解析式,并作出其图像;
(2)若小张家十月份交纳水费90元,求他家十月份的用水量.
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/8e5a27286e86b63fd4f7354a4183c400.png)
(2)若小张家十月份交纳水费90元,求他家十月份的用水量.
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名校
解题方法
5 . 设函数
若
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/9764fea0-addf-4842-b5b6-a16ccec37311.png?resizew=321)
(1)求函数
的解析式;
(2)画出函数
的图象,并指出函数的定义域、值域、单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271d043b44e03bd9cffabd1e81b61c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443e10e57d010ed3877b68351d56d2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22a5fa62ba8d49ec14d0b5e9b8dabf7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/2/9764fea0-addf-4842-b5b6-a16ccec37311.png?resizew=321)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c73c4413b00222e2fdcdd5860c6856.png)
(1)求
,
(2)画出函数的图像
(3)若
,求x的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c73c4413b00222e2fdcdd5860c6856.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e492020b86c090767f34fac06d93a86a.png)
(2)画出函数的图像
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad56942439368d413f74e0ab7d9fb23c.png)
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7 . 已知函数
.
(1)若
,求
.
(2)在直角坐标系中作出函数图象,并写出单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2af3b6f35324a1be052b9fd8e3adb64.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907e4ba6d5f2eea68442def1911957fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在直角坐标系中作出函数图象,并写出单调区间.
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名校
8 . 已知函数
,
(1)作出函数
图像的简图,请根据图象写出函数
的单调增区间;
(2)求解方程
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d6c3594e9c40329851dda894a27b7c.png)
(1)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad56942439368d413f74e0ab7d9fb23c.png)
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名校
解题方法
9 . 已知函数
,
(1)若
,求
的值;
(2)在平面直角坐标系中,作出函数
的草图.(需标注函数图像与坐标轴交点处所表示的实数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce7def019f31f573e49dd2b4bee14a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b2055b9b62e846b03b3d06a4ce2a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在平面直角坐标系中,作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
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10 . 已知
,
(1)求f(
),f [f (-
)]值;
(2)若f (x)=
,求x值;
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572446699208704/1572446705188864/STEM/2e4d6b3a5a264bb8822e35b669ceba8c.png?resizew=216)
(3)作出该函数简图(画在右图坐标系内);
(4)求函数的单调增区间与值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7024a82ab6f27d3ba682ce882de75af1.png)
(1)求f(
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572446699208704/1572446705188864/STEM/5924683a797b4963b8a842a6f1b74bcf.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572446699208704/1572446705188864/STEM/5c4095aa33794c4ca267514d51c06a0e.png?resizew=16)
(2)若f (x)=
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572446699208704/1572446705188864/STEM/44ab13d22d0949d1aaf819ea420da4e7.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572446699208704/1572446705188864/STEM/2e4d6b3a5a264bb8822e35b669ceba8c.png?resizew=216)
(3)作出该函数简图(画在右图坐标系内);
(4)求函数的单调增区间与值域.
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