1 . 已知二次函数
的图象过原点,且满足
.
(1)求
的解析式;
(2)在平面直角坐标系中画出函数
的图象,并写出其单调递增区间;
(3)对于任意
,函数
在
上都存在一个最大值
,写出
关于
的函数解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa7ce6983a3147fee5418459cf7d7ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/fe85e3ab-a1f2-4264-ae25-1cb2449037d3.png?resizew=200)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)在平面直角坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f790223ffd7df9fb44eb11a4c4ce6542.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1553f685ec1fa7f96ceb99456d00c335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f790223ffd7df9fb44eb11a4c4ce6542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4712903dc7b8c313dcb7578d641c43b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
2 . 函数
,其中
为常数,
有
这5个不同的实数解,并且有
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/070c94df-7839-4210-8cfa-fc6aa2f54f40.png?resizew=180)
(1)在坐标系中画出函数
的图象,并求
的取值范围(用
表示);
(2)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c2ec14fe30c6b37be49ff7e1a5a9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195f9cb9c1ca84756dd98afdc784ead9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acd5e05f89802149b8b810c24d6ac73.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/070c94df-7839-4210-8cfa-fc6aa2f54f40.png?resizew=180)
(1)在坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06cee0376e2e795f9ab3740e1304781c.png)
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解题方法
3 . 已知函数
是定义在
上的奇函数,且
图象如图所示.
(1)根据奇函数的对称性,在如图的坐标系中画出
时图象;
(2)①求当
时,
的解析式;
②说明当
时,
的单调性并用单调性定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3549d9f830745a7408e1c3c1cb3c29a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/05a53d47-2ce9-4987-8317-f8ac4d606c0d.png?resizew=168)
(1)根据奇函数的对称性,在如图的坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
(2)①求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
②说明当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc95bc46e0aa25342600533d9a6082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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解题方法
4 . 已知函数
.
(1)画出函数
的图象,并写出函数
的值域及单调区间;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/b8511c19-24a7-4003-850f-eeaa5809bd99.png?resizew=163)
(2)解不等式
;
(3)若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32648060f5e3e810c65f962fa2ea41b0.png)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/b8511c19-24a7-4003-850f-eeaa5809bd99.png?resizew=163)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476e65208aaf36809ee0d65fc61c4dbb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a743e9d797611bdc5fea0621668bb78c.png)
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名校
5 . 已知函数
为定义在
上的奇函数,且
.
(1)求
的解析式;
(2)设
,
(ⅰ)画出函数
的大致图像,并求当
时
的值;
(ⅱ)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db72b5449d97f2b7a27bec1f51dcade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe286322514ef42c902f95b1d2dd838.png)
(ⅰ)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b82c43ecb40fa763214e98b86b70219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9e53433876df2f18d3955a8e4ca2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
6 . 已知定义在R上的奇函数
,当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/a17a9948-6bf6-4aa1-b935-475ffba8ce10.png?resizew=156)
(1)在给出的坐标系中画出
的图象(网格小正方形的边长为1);
(2)求函数
在R上的解析式,并写出函数
的值域及单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15308be822e4af7bc4054e7aa4c50e80.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/22/a17a9948-6bf6-4aa1-b935-475ffba8ce10.png?resizew=156)
(1)在给出的坐标系中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
解题方法
7 . 已知
是
上的奇函数,且当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/52d38c14-7d26-48c7-9e2d-4ff5e11c23b6.png?resizew=189)
(1)求
;
(2)求
的解析式;
(3)画出
的图象,并指出
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f26ccb55fcd29bbbacb32598b852910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/52d38c14-7d26-48c7-9e2d-4ff5e11c23b6.png?resizew=189)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a57e7e65245a4d173c5d0bc3c34e45.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
您最近一年使用:0次
解题方法
8 . 在密闭培养环境中,某类细菌的繁殖在初期会较快,随着单位体积内细菌数量的增加,繁殖速度又会减慢.在一次实验中,检测到这类细菌在培养皿中的数量y(单位:百万个)与培养时间x(单位t小时)的关系为:
根据表格中的数据画出散点图如下:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/4b55fe90-b44c-4b66-8702-6e5692384d6f.png?resizew=210)
为了描述从第2小时开始细菌数量随时间变化的关系.现有以下三种函数模型供选择:①
,②
,③
.
(1)选出你认为最符合实际的函数模型,并说明理由;
(2)请选取表格中的两组数据,求出你选择的函数模型的解析式,并预测至少培养多少个小时,细菌数量达到5百万个.
x | 2 | 3 | 6 | 9 | 12 | 15 |
y | 3.2 | 3.5 | 3.8 | 4 | 4.1 | 4.2 |
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/4b55fe90-b44c-4b66-8702-6e5692384d6f.png?resizew=210)
为了描述从第2小时开始细菌数量随时间变化的关系.现有以下三种函数模型供选择:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07bc29af18b7ac9918932b1ecae6e084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0e2f7981f0b3276f7c2d781bc999b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20137e9e81b0fd121c76e1f48a950599.png)
(1)选出你认为最符合实际的函数模型,并说明理由;
(2)请选取表格中的两组数据,求出你选择的函数模型的解析式,并预测至少培养多少个小时,细菌数量达到5百万个.
您最近一年使用:0次
名校
解题方法
9 . 函数
是定义在R上的奇函数,当
时,
.
(1)求函数
在R上的解析式;
(2)在坐标系里画出函数
的图象,并写出函数的单调递减区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56785f54453abeb59d7cbd09bfb4ec7f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)在坐标系里画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/59ba868a-1659-4b0f-8780-d3a2edf808ea.png?resizew=239)
您最近一年使用:0次
2023-10-26更新
|
441次组卷
|
3卷引用:四川省成都市蓉城名校联盟2022-2023学年高一上学期期中联考数学试题
10 . 已知幂函数
的图象过点
,设函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/cd4263a7-d085-4bf6-94e2-f246dc892b0d.png?resizew=183)
(1)求函数
的解析式、定义域,判断此函数的奇偶性;
(2)根据“定义”研究函数
的单调性,画出
的大致图象(简图),并求其值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e5abce9e520b37572b68141940bbf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/687c95902f2c7a5cb9808ace73b7bbad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/cd4263a7-d085-4bf6-94e2-f246dc892b0d.png?resizew=183)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据“定义”研究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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