解题方法
1 . 以下给出了4个命题:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0aa9d781436ea046ee072ca8482f5b.png)
,
;
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df03c12741f6ac84b451569c55464ebe.png)
,
;
(3)若奇函数
在
上单调递增,则它在
上单调递减;
(4)若偶函数
在
上单调递增,则它在
上单调递减;
其中真命题的个数为( )
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0aa9d781436ea046ee072ca8482f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d314f8771046da1298311369ad35232d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df03c12741f6ac84b451569c55464ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a678cd018f89c3518645bc8439805ce.png)
(3)若奇函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b2e67cd10ebbced3d964ab0dc5c298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
(4)若偶函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715d69eba6fe55144b769fa15f06124.png)
其中真命题的个数为( )
A.4 | B.3 | C.2 | D.1 |
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解题方法
2 . 已知定义域是全体实数的函数
满足
,且
,
,现定义函数
,
为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e655c76c191ba640ea82379a3f2aa6.png)
,其中
,那么下列关于
,
叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0ee9a4b4b53a26c41ff6f41bf29119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443f99d650e24d53e95549a20461384e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d4bf50b179da87140027afcb50ea7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c014250dc069a51f14c59ef14b8e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787903ff7c475c8dac69a17a9063586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e655c76c191ba640ea82379a3f2aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed54e91426a6381c9e527f5bed60f3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99074f989e74d5ff306b4b7b7a379c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c014250dc069a51f14c59ef14b8e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787903ff7c475c8dac69a17a9063586.png)
A.都是偶函数且周期为![]() |
B.都是奇函数且周期为![]() |
C.都是周期函数但既不是奇函数又不是偶函数 |
D.都不是周期函数 |
您最近一年使用:0次
2021-07-15更新
|
239次组卷
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2卷引用:上海市文来高中2023届高三上学期期中数学试题
解题方法
3 . 平阳木偶戏又称傀偏戏、木头戏,是浙江省温州市的传统民间艺术之一.平阳木偶戏是以提线木偶为主,活跃于集镇乡村、广场庙会,演绎着古今生活百态.其表演形式独特,活泼多样,具有浓厚的地方色彩和很高的观赏性与研究价值.现有一位木偶制作传人想要把一块长为4dm(dm是分米符号
,宽为3dm的矩形木料沿一条直线MN切割成两部分来制作不同的木偶部位.若割痕
线段
将木料分为面积比为
的两部分
含点A的部分面积不大于含点C的部分面积,M,N可以和矩形顶点重合
,有如下三种切割方式如图:①
点在线段AB上,N点在线段AD上;②
点在线段AB上,N点在线段DC上;③
点在线段AD上
点在线段BC上.设
dm,割痕
线段
的长度为ydm,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/72438175-47be-47a8-93b5-a1e588dc07e1.png?resizew=492)
(1)当
时,请从以上三种方式中任意选择一种,写出割痕 MN的取值范围
无需求解过程,若写出多种以第一个答案为准![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacbf66f3de4156af7ddbbb9a0aa3555.png)
(2)当
时,判断以上三种方式中哪一种割痕MN的最大值较小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df41c4d9e31986006fad687fe3b5925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a35a2c8738f1a15e8a775c3a7150af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7126e9f44dcb1ca933f3e1885c1d7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e787bb792dcd936cb4e87023c95011b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df41c4d9e31986006fad687fe3b5925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/72438175-47be-47a8-93b5-a1e588dc07e1.png?resizew=492)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aacbf66f3de4156af7ddbbb9a0aa3555.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
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4 . 已知函数
,
下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa0b4ccc2f727ce19611387c28710db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a119b058508e7d4618a0a0e399b460.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2021-12-25更新
|
210次组卷
|
2卷引用:广东省清远市四校联盟2022-2023学年高一上学期期中数学试题
5 . 对于分别定义在
,
上的函数
,
以及实数m,若存在
,
,使得
,则称函数
与
具有关系
.
(1)分别判断下列两组函数是否具有关系
,直接写出结论;
①
,
;
,
;
②
,
;
,
;
(2)若
与
具有关系
,求m的取值范围;
(3)已知
,
为定义在R上的奇函数,且满足:
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
求证:
与
不具有关系
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4413796ac3d5ca067bf70334101f5440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3ac1b540727626af78788a8e5f15de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb566e204173c8aab153deea56647d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834925e383a1e904951eea76b55bcb4f.png)
(1)分别判断下列两组函数是否具有关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d8bc28ee110a9540f383828b7d245.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5466c28592d45ca35059382b351d583f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47c01925c796e12f2729fdfd7ba0393.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a768cc949e4d1ca3effaa7f82b2156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52e17441c2714d5452bf0f8a4a8bb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834925e383a1e904951eea76b55bcb4f.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a78355986534b6e50bd7cabc9290a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d34920b65547eb53779a49ef2274167.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aed3b4ee9510062c8e9aa0e0ffdfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37945d8782048ba94d099fa059fbfb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0127f7421ce1839e335f091d730736af.png)
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解题方法
6 . 若函数
满足在定义域内存在t,使得
成立,则称函数
具有性质M;若函数
对任意实数m,n恒有
,则称函数
具有性质N.
(1)请从下列三个函数:①
(
),②
(
),③
(
)中选择一个,判断是否具有性质M,并说明理由.
(2)函数g(x)具有性质N,且当
时,
,又
.若不等式
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2f84a6e2b68badd47734f36fd546d1.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/d18e9aa1a871a46e1ee008619ce1e4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)请从下列三个函数:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(2)函数g(x)具有性质N,且当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f0423d18d7e23eaccf252ce1a32e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bbe3347e0eaae59ce49aa7e73f0206.png)
您最近一年使用:0次
2021-12-04更新
|
198次组卷
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2卷引用:江苏省扬州市仪征市精诚高级中学2022-2023学年高一上学期期中模拟考试数学试题
名校
解题方法
7 . 已知函数
.
(1)填写下表,在给出的坐标系中画出函数图像(不写过程,直接画图):
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/322f9fab-fddd-4f51-b0b7-80e00e44d282.png?resizew=241)
(2)观察图像,函数
的图像关于_________对称,用数学符号表示为_________.
(3)写出函数
的图像关于直线
成轴对称图形的充要条件,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cc6aecaf7a967b8dfbbeb2892db93d.png)
(1)填写下表,在给出的坐标系中画出函数图像(不写过程,直接画图):
![]() | -1 | 0 | 2 | 3 | |
![]() | 1 |
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/322f9fab-fddd-4f51-b0b7-80e00e44d282.png?resizew=241)
(2)观察图像,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
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8 . 周期信号在电子技术领域具有重要作用.某电路中,一个元件的输入电流是时间t的函数,其解析式为:
,其中参数,m均为常数,且
,
;这个元件的输出电流为:
,记T为电流
的最小正周期,在
内,记满足
的t的区间的长度之和为
,称
为电流
的“占空比”.给出下列四个结论:
①若
,
,则电流
的“占空比”为
;
②保持
的值不变,电流
的“占空比”随m的增大而增大;
③保持m的值不变,电流
的“占空比”随
的增大而减小;
④保持
的值不变,记当
和
时,电流
的“占空比”分别为
和
,则
.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04838c5d453382e555f150b01e301c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c857a71e0ca361a20267b465afc92794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95526b4e6c90f5c488465da2deae916c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3edb4782d23de001cc3fbabff6898d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bedd011a1815cc862756a0f2d9d4ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41309c6138c8c71cd53c86eb95cfdee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0a60c4d93d1233896b5a718875dc6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3edb4782d23de001cc3fbabff6898d5.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3edb4782d23de001cc3fbabff6898d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3edb4782d23de001cc3fbabff6898d5.png)
③保持m的值不变,电流
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3edb4782d23de001cc3fbabff6898d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
④保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a87269f9f7542d4aa50b3911b3ebad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fb74793a4e04ba65a0536e568c25e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3edb4782d23de001cc3fbabff6898d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a85ea4968343b0d94ed2fe01b535.png)
其中所有正确结论的序号是
您最近一年使用:0次
解题方法
9 . 已知函数
.
(1)若
,求
与
值;
(2)由(1)的计算结果猜想函数
在
时满足什么性质,并证明你的猜想;
(3)证明:
在区间
上单调递增,在区间
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3cc003c247a071289c554673717f6e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15a13b4190ac3d5feaee27a4c97b21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2b9eeb64b8ac9babf5aa14fa12cefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403396007517994ef540b2a13cb4d9d6.png)
(2)由(1)的计算结果猜想函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15a13b4190ac3d5feaee27a4c97b21b.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff618b9a8dfc677e2f6782ab989d14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b28c80843f3bb905547e681859e8d3c.png)
您最近一年使用:0次
2022-11-16更新
|
96次组卷
|
2卷引用:重庆市双福育才中学校2022-2023学年高一上学期期中数学试题
10 . (1)用描点法在同一个坐标系下画出函数
和
的图象;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/607c02af-4d14-453b-aa80-044f7d5eb362.png?resizew=269)
(2)观察这两个函数的图象,从函数性质(定义域、值域、奇偶性、单调性)的角度,你能发现哪些共同点?
(3)请你用符号语言精确地描述以上共同点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065694d76ffd5570656436d9edfd75ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e9d77085e58ed83a369ad1490c9f18.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/607c02af-4d14-453b-aa80-044f7d5eb362.png?resizew=269)
(2)观察这两个函数的图象,从函数性质(定义域、值域、奇偶性、单调性)的角度,你能发现哪些共同点?
(3)请你用符号语言精确地描述以上共同点.
您最近一年使用:0次