名校
解题方法
1 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/e762b135-b90f-41e9-9be8-77f0050e636e.png?resizew=207)
(1)直接写出方程
的解;
(2)在坐标系中,画出
的大致图像;(注意要画在答题纸上)
(3)根据图像,讨论关于
的方程
解的个数;
(4)若方程
有四个不同的根
,直接写出这四个根的和;
(5)直接写出函数
的单调增区间;
(6)直线
与
的图像有三个交点时,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113eff4fc6357344d826ff081714339d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/e762b135-b90f-41e9-9be8-77f0050e636e.png?resizew=207)
(1)直接写出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)在坐标系中,画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)根据图像,讨论关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
(4)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
(5)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(6)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07565f10847840e0fb07b05218ad17fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2022-11-10更新
|
373次组卷
|
2卷引用:第8章 函数应用 单元综合测试卷-2022-2023学年高一数学新教材同步配套教学讲义(苏教版2019必修第一册)
名校
解题方法
2 . 已知函数
满足
,函数
是
上单调递增的一次函数,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/6ce63b98-53d2-429f-8456-4d507c4a0850.png?resizew=265)
(1)证明:
,
;
(2)已知函数
,
①画出函数
的图像;
②若
且
,
,
互不相等时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f6b132b0f8a8ce00642f297ab0e7a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339b85cca0100adc23472c143f9a5a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4191aed4e079966f89c12cc54a4dbbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/6ce63b98-53d2-429f-8456-4d507c4a0850.png?resizew=265)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5cb16179eee83ee4c01f1bd9b8371d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee737b76b747390c423bec199aaf37c.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e9e3ca0b965ebe07a3e11d7f2933b.png)
①画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d89c7d892826f42b6fc9b8f7f903b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fdeba282b028321696be7f90f2cbfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3aa688caadfeb5bdf9c7dfecb5afa31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb14e2fe3859d5aecf636054ee65d77.png)
您最近一年使用:0次
2022-10-20更新
|
677次组卷
|
3卷引用:江苏省连云港市灌南高级中学2022-2023学年高一上学期解题能力大赛数学试题
2022高一·江苏·专题练习
解题方法
3 . 求下列函数的定义域、值域,并画出图象:
(1)
;
(2)
;
(3)
;
(4)
;
(5)
;
(6)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979517870cac149768c3a9bf10c2671f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07e744f4e3a2720878265d3651f2e02.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46aa18b552bea10252bfa82b604f33a6.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5dbfac684b9901a16ae61dbaa0f817.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0826fcb806662f344814a7c4dcfd5263.png)
(6)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5397ee1eb6d157f6ec1e7a878f8d16e.png)
您最近一年使用:0次
名校
4 . 已知函数
(
).
(1)用分段函数的形式表示函数
;
(2)请在方格坐标系中画出函数
的图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fdb656c4884a095fda01d1c2745bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c1eee20ce660b25caf95a657584ea3.png)
(1)用分段函数的形式表示函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)请在方格坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/ceb17501-aaf8-43a4-943f-eb76a7631f14.png?resizew=188)
您最近一年使用:0次
2022-12-05更新
|
149次组卷
|
5卷引用:第13讲 函数的表示方法-【暑假自学课】2022年新高一数学暑假精品课(苏教版2019必修第一册)
(已下线)第13讲 函数的表示方法-【暑假自学课】2022年新高一数学暑假精品课(苏教版2019必修第一册)江苏省盐城市大丰区新丰中学2021-2022学年高一上学期期中数学试题山东省菏泽市定陶区明德学校(山大附中实验学校)2022-2023学年高一上学期第一次阶段性考试数学试题陕西省榆林市神木中学2021-2022学年高一上学期第一次测试数学试题吉林省乾安县第七中学2021-2022学年高一上学期第一次质量检测数学试题
5 . 函数
,
(1)画出函数的图象;
(2)根据图象指出函数的单调区间和最大值、最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3d86c3302c2695fd4191c22ac0a4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abe2b125a01138db12b8bff1d2833a9.png)
(1)画出函数的图象;
(2)根据图象指出函数的单调区间和最大值、最小值.
您最近一年使用:0次
6 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/ca4b8201-2423-4f99-b0a2-0877f4646fd7.png?resizew=286)
(1)若
在
上的最小值记为
,求
的解析式;
(2)画出
的函数图像,并根据图像写出
的最大值;
(3)若
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb4b18d9a64771883d87596c57cb6b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/6/ca4b8201-2423-4f99-b0a2-0877f4646fd7.png?resizew=286)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(2)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7780f324bba98e6bf3218daf3e8f8d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 如图,
是边长为2的正三角形,记
位于直线
(
)左侧的图形的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/b92321c7-e5b4-47f2-8aa7-6540e15b7ba3.png?resizew=112)
(1)求函数
的解析式;
(2)画出函数
在区间
上的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9cec0474c43086ea39cb457048313c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/b92321c7-e5b4-47f2-8aa7-6540e15b7ba3.png?resizew=112)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9b65c51e37f40211b876be02105701.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9b65c51e37f40211b876be02105701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
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8 . 辆高速列车在某段路程中行驶的速率v(单位:
)与时间
(单位:
)的关系如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/2c6d2232-c192-4d32-aa91-7fd38f643db6.png?resizew=399)
(1)求梯形
的面积,并说明所求面积的实际含义;
(2)记梯形
位于直线
的左侧的图形的面积为
,求函数
的解析式,并画出其图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ca55c030e7d88040525c4fb9a278f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933311c0c090e1138e4dd388b7adf8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/2c6d2232-c192-4d32-aa91-7fd38f643db6.png?resizew=399)
(1)求梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
(2)记梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c67d2fa597fb81c8943ddfcd011227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b35d2aa8af392c852eb9b1cb1732bd.png)
您最近一年使用:0次
名校
9 . 如图,在边长为4的正方形
的边上有一点
,沿着折线
由点
(起点)向点
(终点)运动.设点
运动的路程为
,
的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/9d5ef4c8-85e7-469d-864e-7b6927b26b3c.png?resizew=150)
(1)求
与
之间的函数关系;
(2)画出
的图象;
(3)求函数
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58140fed320b904794b2b771f235950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/9d5ef4c8-85e7-469d-864e-7b6927b26b3c.png?resizew=150)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.
(1)将函数
写成分段函数的形式,并画出图象;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/db00cdce-6193-4400-92e1-6062cc7b60c5.png?resizew=178)
(2)利用图象回答:当
为何值时,方程
有一解?两解?三解?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c2837ca79dac067e0872eded379e91.png)
(1)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c2837ca79dac067e0872eded379e91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/db00cdce-6193-4400-92e1-6062cc7b60c5.png?resizew=178)
(2)利用图象回答:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0546cf3869d3cf439a2e1ff2306608fc.png)
您最近一年使用:0次