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1 . 圆形是古代人最早从太阳、阴历十五的月亮得到圆的概念的.一直到两千多年前我国的墨子(约公元前468-前376年)才给圆下了一个定义:圆,一中同长也.意思是说:圆有一个圆心,圆心到圆周的长都相等.现在以点
为圆心,2为半径的圆上取任意一点
,若
的取值与x、y无关,则实数a的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9eb2780c00dcea20ac3e337141071e.png)
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2023-10-14更新
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654次组卷
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4卷引用:上海市洋泾中学2024届高三上学期10月月考数学试题
2 . 对于函数
及给定的实数
,若存在正实数t使得函数
在区间
和
上同为增函数或同为减函数,则称函数
为区间
上的
函数;
(1)已知
,请指出函数
是否为区间[0,1]上的
函数(不需要说明理由);
(2)已知
,且函数
是区间
上 的
函数,请写出t的所有取值,并说明理由;
(3)若函数
既是区间
上的
函数又是区间
上的
函数,当α、β取遍所有可取的值时,求出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1b52a92fd3dc776c43fa5ff1e3be9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa38149578f22f9e1e2bd481dade72de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40af4dded142fd56ff3dc505a3751d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1b52a92fd3dc776c43fa5ff1e3be9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3c22079495aace7a6e1a6c7d36f6d9.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42acea836df9ca7c237b52df778c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1396f59915eb245c39a974fc778e9cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d4235095bdb902078a2a515af9e3d2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c599ff76117b8493cb817c03329786a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3c22079495aace7a6e1a6c7d36f6d9.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab4f92366ae95454b50ff6219155900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92de12037343c43634104d23fa4e08c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882427a7e4ab8a9d62922051b707049a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd53169f0e89a6bccdbc4603bc1cff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd12996c1ba5de97286e5bb2dc1e90f.png)
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3 . 设
.
(1)若
,求出满足条件的角
的解集;
(2)当
时,若存在
使关于
的方程
在
时均有解,求实数c的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875fbccb50c0ada9183ef37262aac370.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a7d6528f2fd79da5ffc9bfbf97b0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e59409c55e271b690491f42fc1f6b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffe44aa519044b273b0e48286134406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875fbccb50c0ada9183ef37262aac370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8e9f49445220aae9d068ea8b1c617.png)
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