名校
1 . 已知函数
,
,如果对于定义域D内的任意实数x,对于给定的非零常数P,总存在非零常数T,恒有
成立,则称函数
是D上的P级递减周期函数,周期为T;若恒有
成立,则称函数
是D上的P级周期函数,周期为T.
(1)判断函数
是R上的周期为1的2级递减周期函数吗,并说明理由?
(2)已知
,
是
上的P级周期函数,且
是
上的严格增函数,当
时,
.求当
时,函数
的解析式,并求实数P的取值范围;
(3)是否存在非零实数k,使函数
是R上的周期为T的T级周期函数?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99d26e65e02ba8ec1b10529e5a0253c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab21d3bab25b356abae92e6ff08f7d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499f8a6c1737ed4c552a93b0b64e4958.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac920b4fb011075ccd75d7807cca5a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2645398c3946e1a9282c219824f167d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc079255ea327cb71b3bcfe48693d17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37475d9dc070faa59a1801b59d2ec2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)是否存在非零实数k,使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a3ca0dd34a3cd5ca9a5c5055ceee23.png)
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2022-04-26更新
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10卷引用:上海市复旦大学附属中学青浦分校2022-2023学年高一下学期3月月考数学试题
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2 . 已知函数
的图象是自原点出发的一条折线,当
(
)时,该图象是斜率为
的线段,其中常数
且
,数列
由
(
)定义.
(1)若
,求
,
;
(2)求
的表达式及
的解析式(不必求
的定义域);
(3)当
时,求
的定义域,并证明
的图象与
的图象没有横坐标大于1的公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed2be63fc4c8ab5ad34817459fe7e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6961967d7e48061a9cbb14f597e73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8212e307836cb33f16575e23f6b808e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406185f4ad8bcd99e23adc8d289088ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04a87082c00feca63aaea95a41f30d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6961967d7e48061a9cbb14f597e73d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bdc8d2686a05f12a2ba8a7e3b01be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
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