1 . 已知函数
,
.
(1)当
时,求函数
的对称中心;
(2)若
为奇函数,不等式
在
上恒成立,求实数m的取值范围;
(3)若
过点
,设
,若对任意的
,
,都有
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2626a5bdd100424d2416a665ba0e9518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf8749fbcb186eb686926e74408ae62.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d47dbed3333b180fce58a6d9e440f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f8ac22194d05c73c0398ec74b1aa89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ca34d82c95713100598611fc59b4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61163de79f28694431516e0e72f0cb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28950ab83fa7d677e639b6680cb016ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57045228fec057c04c8a9a3423ee9d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94a283921f59e507c96d0b6fbbe8fa4.png)
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2 . 已知函数
,其中
,
图象上对称中心到相邻最近对称轴之间的距离为
.
(1)求
的解析式和单调递增区间;
(2)若将函数
图象上所有点的横坐标变为原来的2倍(纵坐标不变),得到函数
的图象,再向左平移
个单位,得到函数
的图象,求函数
在
上的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2120d916a5c0f132316080c347ff2123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220ad5eaba4ed61218a085819d5c4ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef023abc92ef73106fe81762d8ae87d.png)
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解题方法
3 . 下列说法正确的是( )
A.函数![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.已知函数![]() ![]() ![]() |
您最近一年使用:0次
2024-01-20更新
|
544次组卷
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2卷引用:重庆市第一中学校2023-2024学年高一上学期期末考试数学试题
名校
解题方法
4 . 若不等式对
恒成立,则实数
的取值范围是
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解题方法
5 . 已知函数
(
)有最大值为2,且相邻的两条对称轴的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
的解析式,并求其对称轴方程;
(2)将
向右平移
个单位,再将横坐标伸长为原来的
倍,再将纵坐标扩大为原来的25倍,再将其向上平移60个单位,得到
,则可以用函数
模型来模拟某摩天轮的座舱距离地面高度H随时间t(单位:分钟)变化的情况.已知该摩天轮有24个座舱,游客在座舱转到离地面最近的位置进仓,若甲、乙已经坐在a,b两个座舱里,且a,b中间隔了3个座舱,如图所示,在运行一周的过程中,求两人距离地面高度差h关于时间t的函数解析式,并求最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0912273ca8068fe8bba670c8a1258a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4441ad594b4f1ecf4ddfa411f10327c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3b61f06b89016d84dac97e1939792b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667c4923ac23ec536f06edc10fb0160d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ad8d8a8a678a8cdea5961968d256c8.png)
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2024-01-18更新
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523次组卷
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3卷引用:重庆市渝中区巴蜀中学校2023-2024学年高一上学期1月期末数学试题
解题方法
6 . 已知函数
的定义域为
,若存在实数
,使得
,都
满足
,则称函数
为“三倍函数”.
(1)判断函数
是否为“三倍函数”,并说明理由;
(2)若函数
,
为“三倍函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ceebb6c5513dcad6f39500e269807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be56b7ebc5ff4806ce9e4861fe74be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59a97f9ce032517db9f401e2467315d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe5dd06b9ed45ad661ce1376283a21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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名校
7 . 如图,正方形
的边长为2,
,
分别为AB,BC的中点.以O为圆心,OA为半径的圆弧
上有一点P,T、S两点分别在线段AB、BC上,使得四边形SBTP为矩形.
绕
点逆时针旋转
后使其与
点重合,求
;
(2)求矩形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0a98828cab1d9bd9184aa53750bd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(2)求矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569720fe517e7b8f4bca5144f71d4352.png)
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8 . 已知的部分图象如图所示,当
时,
的最大值为
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解题方法
9 . 某学校在校园美化、改造活动中需要在半径为50m,圆心角为
的扇形空地
的内部修建一个矩形观赛场地
.如图所示,M为弧
的中点,
与
和
分别交于点E、F,记
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/3311fba1-9093-4671-ba6d-004babcd5c42.png?resizew=119)
(1)求矩形
面积S与
之间的函数关系
;
(2)当
取何值时,矩形
的面积最大,并求出这个最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6c71a0da6a878a5b12bf8a8e784645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b99701da0b9602dca0d8bf78bf920a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/3311fba1-9093-4671-ba6d-004babcd5c42.png?resizew=119)
(1)求矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812ddf68e35feaa9236cfa79633f0113.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
10 . 已知函数
,
,函数
的图象上两相邻对称轴之间的距离为
,_________.请从以下三个条件中任选一个补充至横线上.
①函数
的图象的一条对称轴为直线
;
②函数
的图象的一个对称中心为点
;
③函数
的图象经过点
.
(1)求函数
的解析式;
(2)将
图象上所有点的横坐标伸长到原来的2倍,纵坐标不变,再向右平移
个单位得到
的图象,若对任意的
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c3ad6bbf0f6241fab7042124594db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3731e4fe7dbd8899acb023f8647b71af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a177d7c16a192fa12cc85a3b7701ad.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b2b096238bd6eac8cd1ab2c4348fb9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e74fc7479e44217bfa27dbd75992b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351fd422a73cc7a4b4790b59493b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-11更新
|
306次组卷
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4卷引用:重庆市北碚区2023-2024学年高一上学期期末学业水平阶段质量调研抽测数学试题
重庆市北碚区2023-2024学年高一上学期期末学业水平阶段质量调研抽测数学试题(已下线)高一数学开学摸底考 02-人教A版2019必修第一册全册开学摸底考试卷陕西省汉中市勉县第二中学等校2023-2024学年高一下学期第一次月考(3月)数学试题(已下线)专题03y=Asin(ωx+φ)的综合性质期末8种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)