名校
解题方法
1 . 函数
(其中
,
,
)的图象如图所示,则函数
的解析式为______ ,若将该函数
的图象上的各点的横坐标伸长为原来的3倍(纵坐标不变)得到函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f592268b2f9318b2c70ab505f5776cd0.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec89c3bc454d209007c2b29baeeb3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad57bb09b32ff941dde57f000b82fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f592268b2f9318b2c70ab505f5776cd0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/a85475b4-ad95-43b6-888c-c4804fa116ef.png?resizew=139)
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2 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0460e84f6313878f1aba62275fd86044.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395f83921ac830a78424fbec0ca00056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0460e84f6313878f1aba62275fd86044.png)
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3 . 若定义域为
的奇函数
满足
,且其图象过点A,点A为函数
(
且
)的图象所过定点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c614528ecc55866008161dae107b748d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fba6a56ed9da2f62e0d243a9cb23a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a580cb582c782207eea3e1387cc627.png)
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4 . 已知
,
且
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e189dbc979fad6bf8ca03ac1388cbac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c781e4cba6577e9fa4a9ea22407eb93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264977ec89caac6d99ad56d8ae8b142d.png)
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5 . 设椭圆
的焦点为
是椭圆上一点,且
,则
的面积为__________ (用含
或
的式子表示即可)若
的外接圆和内切圆的半径分别为
,
,当
时,椭圆的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ed463bf16c78a4bbb9d3acff922afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db634c178cd7bffbd4cb886e3f2cca22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f773c218d2466baef4f278de9d0d6f7c.png)
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6 . 已知幂函数
在
上是减函数,
.若
,则实数
的取值范围为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20d7ceb5302e7bf0767e089dc79374e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d37a57420d5e3091ddf17df03b6fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 已知函数
,满足
的
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d81f8c938a9c413502f08e391fe5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366a46193d8c0045cce47b2edca76758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 设
,
表示不超过
的最大整数,关于函数
有下列结论:
①
是奇函数;②
的值域为
;③
在区间
上单调递增;④
,
,其中正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602c6c52cae281dc7dad9bc7cc07d6bb.png)
①
![](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/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac47c1b6230edf33b5a1c76b75025de.png)
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9 . 已知直线
经过点
,且点
到直线
的距离相等,则直线
的方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69abe959988e4c8c0739f5857ccfb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccb2d5086ddda99f9c1bee4aa1df655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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10 . 已知向量
,若
,则
的值可以是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f322ddf323a68e125a58cd4fa80d5c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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