名校
1 . 对于定义在
上的函数
,如果存在一组常数
,
,…,
(
为正整数,且
),使得
,
,则称函数
为“
阶零和函数”.
(1)若函数
,
,请直接写出
,
是否为“2阶零和函数”;
(2)判断“
为2阶零和函数”是“
为周期函数”的什么条件(用“充分不必要条件”“必要不充分条件”“充要条件”或“既不充分也不必要”回答),并证明你的结论;
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892519541cfba6f2763cd29159bf1b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fb959f16f82835aa68fca9d3f08f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcda6a21da79726f8fb3ba6235b9010f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebef85c05f6d84ceb67d92abf77ba2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
(2)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab7da79b2400cf8125ef040cd056b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b15db96dc89f136a7421e09fc9814.png)
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2 . 已知
,关于x的不等式
的解集为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a42fff822c5f61fec5fcd5c8e86941e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e080d3d338e4398d91b493797eb8ce33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e0a0dde137e24c80d0afeec024f2b6.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-03-14更新
|
812次组卷
|
2卷引用:甘肃省陇南市部分学校2024届高三一模联考数学试题
名校
解题方法
3 . 已知
满足三个条件:①
②
③_______.若这样的
恰好有2个,则③可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236f52e04ddbd7253f44b97c4756ef9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abead4f17037ed14fe3d4cb34c5bc08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
4 . 某种信号的波形可以用函数
的图像来表达.则下列各结论正确的有___________ .
①最小正周期为
;
②对称轴为
,
;
③在
上有9个零点;
④值域
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bc0f07b30932fc48cd902875bed83d.png)
①最小正周期为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
②对称轴为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da2c9afa7bb46a5f8f058720252b050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99074f989e74d5ff306b4b7b7a379c1f.png)
③在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8a4830a9a0993a0710edf448fe7521.png)
④值域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e99bebf8db0d314aacb2cb1f09bf48c.png)
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2022-05-02更新
|
2222次组卷
|
6卷引用:北京市北大附中2021-2022数学高一下学期期中数学试题
北京市北大附中2021-2022数学高一下学期期中数学试题广东省广州市白云中学2024届高三上学期12月月考数学试题广东省珠海市第一中学2024届高三上学期大湾区期末预测数学试题(一)(已下线)考点11 倍(半)角公式及其应用 --2024届高考数学考点总动员【练】(已下线)第10章 三角恒等变换 单元综合测试(难点)-《重难点题型·高分突破》(苏教版2019必修第二册)四川省绵阳市东辰学校2024届高三下学期第二学月考试数学(理科)试题
5 . 如果对于三个数
、
、
能构成三角形的三边,则称这三个数为“三角形数”,对于“三角形数”
、
、
,如果函数
使得三个数
、
、
仍为“三角形数”,则称
为“保三角形函数”.
(1)对于“三角形数”
、
、
,其中
,若
,判断函数
是否是“保三角形函数”,并说明理由;
(2)对于“三角形数”
、
、
,其中
,若
,判断函数
是否是“保三角形函数”,并说明理由.
![](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/071a7e733d466949ac935b4b8ee8d183.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3bf2007903adc64d089a054c2284a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4889b4b46d3cd6dd677d200bdf4914fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de447d5e47448d0f15a7535bf3ce0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)对于“三角形数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dd0c52aca1675c17b9a019aa7901e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfdf1828a8dfbd475598d3c69e86414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49065dba37bda632460abb2929f6ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457eb5e0000350b102d387a80cf3476b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)对于“三角形数”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0643e854e863263f396fa25ab54d44e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae43a9e2f9976ced1f55c62d24c80bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbc8ca5a7888a06f1aab92f76f62a0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588bbf780d49cf4d29802c2e4126f112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
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2021-07-24更新
|
1920次组卷
|
6卷引用:上海市复兴高级中学2020-2021学年高一下学期期中数学试题
名校
6 . 已知集合
,称
为
的第
个分量.对于
的元素
,定义
与
的两种乘法分别为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aa5853722e3158b0f77917726dbc6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e510332893c067eeef1fe76cefa1173.png)
给定函数
,定义
上的一种变换
.
(1)设
,求
和
;
(2)设
,对于
,设
,
对任意
且
,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c34b66a9efd802f743dcc652aa8820.png)
①当
时,求证:
中为0的分量个数不可能是2个;
②若
的任一分量都只能取
或
,设
的第1个分量为
,求
的最小正周期的最小值,并求出此时所有的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16531ec81209cad92180eba890c9b137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a5369bb892f707c3f0a2ac2fa18f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aa5853722e3158b0f77917726dbc6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e510332893c067eeef1fe76cefa1173.png)
给定函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c01c6322201e64d7b9442f99728aa7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056e669d7afaf70e555f1c4fb9192ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12359a62d8ca4edfcecca9909cccfc33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d3de45518fa839fbf8e2426fa8d1f8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc498431c1a7c9e48c3858faf7bfd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1348da718d01114e3db4355c08531c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550a28e39bec7b9d5f8e722f00b44e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec3194cabfe4b369b8ff464bda89964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2aa68223dfc02f39d7d10fa005387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918893290e48bba154bd5a14a805f10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c34b66a9efd802f743dcc652aa8820.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1348da718d01114e3db4355c08531c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be6f009bfb61b11e4f87edb4132de3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ea50db79b18d8700cfa2559ff5e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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