解题方法
1 . 如图所示,在平面直角坐标系
上放置一个边长为1的正方形PABC,此正方形PABC沿
轴滚动(向左或向右均可),滚动开始时,点P位于原点处,设顶点
的纵坐标与横坐标的函数关系是
,该函数相邻两个零点之间的距离为m.
(1)写出m的值并求出当
时,点P运动路径的长度
;
(2)写出函数
的表达式;研究该函数的性质并填写下面表格:
(3)试讨论方程
在区间
上根的个数及相应实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208836dfd77253efa91e9956d0d769a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/c65f43f5-df1a-46a4-b0c6-b9a4320af870.png?resizew=162)
(1)写出m的值并求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f52db3046e7c92b3a7fdd6c34657663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc61760a5002a5e387a33c8b768b292.png)
函数性质 | 结论 |
奇偶性 | |
单调性 | |
零点 | |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f12bc35b1aa8d82897a2ac6acaaabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a23270dc14c9cea8b127f17f554b8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 给定函数
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/ff16be9f-fd82-4290-b3b9-7b4f8348e16a.png?resizew=127)
(1)画出函数
的图象(不需要列表);
(2)
,用
表示
中的较大者,记为
请分别用图象法和解析法表示函数
,并求出
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c13b0a7b3d9aecb84e98d15f89e26ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/ff16be9f-fd82-4290-b3b9-7b4f8348e16a.png?resizew=127)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2541a407e5e65cd230cb1d0954881d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
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2023-10-14更新
|
228次组卷
|
2卷引用:陕西省西安中学2023-2024学年高一上学期第一次月考数学试题
解题方法
3 . 已知函数
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/3d1bd810-67ab-46d9-93e0-a0afa9a3e87b.png?resizew=210)
(1)判断函数
的奇偶性并用定义证明;
(2)用分段函数的形式表示函数
的解析式,并直接在本题给出的坐标系中画出函数
的图像;
(3)用
表示
,
中的较大者,即
,若
,则求
的值 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578b5d562457a6ba731ee5a2dd3b1fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63716f1f42c412f23bfb2f3651638c4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/3d1bd810-67ab-46d9-93e0-a0afa9a3e87b.png?resizew=210)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)用分段函数的形式表示函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c694cf892ee07daa54bdd9f2fb421e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b345ba4baeae1041f7d69ad09dc326c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe57503d720d07a26770942b067d2cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb07ef16a59c3fca5b82ec18b38f75a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/6e78baf3-b1e2-45d8-a73e-b1270132247e.png?resizew=185)
(1)求
,
的值;
(2)在给定的坐标系中,画出
的图象
无需列表![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440a091777c1e606220ad30862b8664b.png)
(3)根据(2)中的图象,写出
的单调区间和值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb07ef16a59c3fca5b82ec18b38f75a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/6e78baf3-b1e2-45d8-a73e-b1270132247e.png?resizew=185)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2518f6b97e516aa2bd548234370fc5.png)
(2)在给定的坐标系中,画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440a091777c1e606220ad30862b8664b.png)
(3)根据(2)中的图象,写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2023-11-23更新
|
170次组卷
|
3卷引用:安徽省滁州市2023-2024学年高一上学期期中联考数学试题
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f649dfa9924afa93b01e625b29892af4.png)
(1)求
的值;
(2)画出函数
的图象,根据图象写出函数
的单调区间;
(3)若
,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f649dfa9924afa93b01e625b29892af4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/089089fe-6a85-433e-9be7-901226b7b3ee.png?resizew=208)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afec19e592ef5542a983b82e0da5275d.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
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2023-11-13更新
|
531次组卷
|
2卷引用:北京市顺义区第二中学2023-2024学年高一上学期期中考试数学试题
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c604e08a0837f160207b05dec72decaf.png)
(1)求
;
(2)若
,求
的取值范围
(3)画出
的图象,并写出函数的单调区间和值域. (直接写出结果即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c604e08a0837f160207b05dec72decaf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/04f311e6-4902-47de-9306-93206a178ea0.png?resizew=179)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe561b2dcc4f0f68fbca0b8cf4cecc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8739b1c13e4375e746a1f7856abfe7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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7 . 已知函数
=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277db553f9cc1dbaa5424321b03daf9e.png)
(1)求
,
的值
(2)在给定的坐标系中,画出
的图像(每格一个单位)
(3)若关于x的方程
无解,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277db553f9cc1dbaa5424321b03daf9e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e1a1611f320c0f358df77aaae3f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a1539c074dbff8cb4198cabeee36ed.png)
(2)在给定的坐标系中,画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce90064385c4633056784c1ae375a2d5.png)
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名校
解题方法
8 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/dbfa2821-50ed-4fbb-b3a9-46ad60ffafde.png?resizew=196)
(1)分别求
,
,
的值;
(2)画出函数
的图象;
(3)求出函数
的定义域及值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3ee2e8db259bb4a5160033c63cf414.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/dbfa2821-50ed-4fbb-b3a9-46ad60ffafde.png?resizew=196)
(1)分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865a84e106d64bec207e497b6663e53e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf82d73eb2a6fe7b44de2b73bcb41467.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2023-11-14更新
|
107次组卷
|
2卷引用:北京市顺义区杨镇第一中学2023-2024学年高一上学期期中考试数学试题
名校
解题方法
9 . 已知对
,都有
,且当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/c2f0b928-6f51-49cc-81ca-9839cb16f5f8.png?resizew=203)
(1)求函数
的解析式,并画出
的简图(不必列表);
(2)求
的值;
(3)求
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb558e17c9818610772917878d82d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4661d318d27ee704fd8b22f34e0773ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/c2f0b928-6f51-49cc-81ca-9839cb16f5f8.png?resizew=203)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea09ab225081c171f6d54afec5ffaad9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39620429c511534bfaa25ead63cd308d.png)
您最近一年使用:0次
2023-11-07更新
|
195次组卷
|
4卷引用:辽宁省阜新市高级中学2023-2024学年高一上学期期中数学试题
解题方法
10 . 已知对
,都有
,且当
时,
.
(1)求函数
的解析式,并画出
的简图(不必列表);
(2)求
的值;
(3)求
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3dfb9993f0852e443ea196e974013d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad8ca0dc9a54c3346d495bb66740b6a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/a2c7f897-ab4c-4bb8-adbc-bcaee5e4cbe8.png?resizew=213)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea09ab225081c171f6d54afec5ffaad9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7da221f28de0d5aa1b62e0d41cab7d9.png)
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