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1 . 在研究函数过程中,经常会週到一类形如
为实常数且
的函数,我们称为一次型分式函数.请根据条件完成下列问题.
(1)设
是实数,函数
,请根据
的不同取值,讨论函数
的奇偶性,并说明理由;
(2)设
是实数,函数
.若
成立的一个充分非必要条件是
,求
的取值范围;
(3)设
是实数,函数
,若存在区间
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9796db5f297d4023eac8d1aa4739c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b744e7cd7496125a9bcd6b756d09ebff.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1944af8ede16275cdcbe721a81870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8aade587301e484fe76bdf87e6d5b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47f8d234c1df11e957b9bd7d3f2da47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe2a076aa933bf55763c67b8734b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af24aeacd2576456cc192826ecd5b107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcc3c97c6d73f7ef44b90ec6f3065ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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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 . 已知两圆
,
.
(1)
和
的圆心分别为
和
,若直线
与线段
有交点,则实数
的取值范围是___________ .
(2)在一张画有直角坐标系的足够大的白纸上画出
和
,并将这两个圆的圆内部分均涂满红色,过原点画一条斜率为
的直线
,沿着
将该纸剪成两张纸,若这两张纸上红色部分的面积相等,则实数
取值的集合为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3482c9faf127d5248037bc7e036ed36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101db7e46ae221a40f0f36891faf3b20.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f49fc6babe4d5eba3b33891e75ec1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在一张画有直角坐标系的足够大的白纸上画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
4 . 已知函数
.
(1)求将函数
的图像进行怎样的平移,能够得到函数
的图像?
(2)若函数
在
上是严格减函数,求实数
的取值范围.
(3)将函数
图像向右平移一个单位,得函数
的图像,已知函数
图像关于
轴对称,且当
时,它与函数
的关系是
.现已知关于
的方程
解集中有七个元素,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
(1)求将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b28fb1035e9ff7766a054b5c86a150.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b28fb1035e9ff7766a054b5c86a150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a8b8044825d59a09d5ff2efdc42981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959d754452ebd9902832a977ddb86491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb9667923104003b76a66d7c3b0a1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f71ef140d15cb1834a91b060df0dfda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b481ee616038c222bc8b2b4d1e4d23a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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