解题方法
1 . 已知
(常数
),则正确的选项为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd87013d484100d4d04cf88a110bafdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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2 . 对任意两个实数a,b,定义
,若
,
,下列关于函数
的说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9e0f7fd210c8ebc45692f5be03db7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad8ca0dc9a54c3346d495bb66740b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c4473159277aed64ea96c4af087954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a5ed61ee16595684717cf82790984a.png)
A.函数![]() | B.方程![]() |
C.函数![]() | D.函数![]() |
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3 . 设正实数
满足
,则当
取最大值时,
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7caaacb4919b6a9636940385869a4198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117def9eb572a35832e631ffd09c97b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32736ef0060aa3293557f14a67615296.png)
A.0 | B.3 | C.![]() | D.1 |
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4 . 单位时间内通过道路上指定断面的车辆数被称为“道路容量”,与道路设施、交通服务、环境、气候等诸多条件相关.假设某条道路一小时通过的车辆数
满足关系
,其中
为安全距离,
为车速(
).当安全距离
取
时,该道路一小时“道路容量”的最大值约为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3ff850adedb33e9572dfbcc31dbff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44f67ab69be2217f7884536cfa53aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53afeaf21f93091b71608d21540be239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f44f67ab69be2217f7884536cfa53aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1611d15c7e1e4ab4a4a61537b3989d8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 下列关系中正确的个数是( )
①
;②
;③
;④
;⑤
;⑥
,
,
或
.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbcfdbb037371ed130cf0666970fdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80443aab83047278ee884b65efeaf493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2123a3f51cee0e592959fb02820b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947853a47a4ec2f143f23b0d6044c22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0543e38340a2412d3638d9c2f4a253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa26ede4564b80c035c146272384bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae7edc45b3c0d2bca0300a72735f82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b712d2890648f86b902b650f494a8e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5806497d3b5ec15d89eef8202d54d7a0.png)
A.2 | B.3 | C.4 | D.5 |
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6 . 某地某路无人驾驶公交车发车时间间隔
(单位:分钟)满足
,
.经测算,该路无人驾驶公交车载客量
与发车时间间隔t满足:
,其中
.
(1)求
,并说明
的实际意义;
(2)若该路公交车每分钟的净收益
(元),问当发车时间间隔为多少时,该路公交车每分钟的净收益最大?并求每分钟的最大净收益.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d7e6e5c1877a2ac639a7ecb0b957cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01010b76f1344143f401238db4043dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bb9c7f10d97c48c974f831336a85b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932894ad4957707dfa342fec39c8e7af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01010b76f1344143f401238db4043dea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6479af5325b584a16a45975b771d98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6479af5325b584a16a45975b771d98.png)
(2)若该路公交车每分钟的净收益
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b8c83cafdb385849a19f505dea155f.png)
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解题方法
7 . 已知函数
是定义在R上的奇函数,且当
时,
,函数
在
轴左侧的图象如图所示,并根据图象:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/7e7eaacf-b856-4a50-ab96-8e9f67ecaab3.png?resizew=157)
(1)画出
在
轴右侧的图象,并写出函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
的单调递增区间;
(2)写出函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
的解析式;
(3)若函数
,求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9a748648e1ab88272407b598bf6447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/7e7eaacf-b856-4a50-ab96-8e9f67ecaab3.png?resizew=157)
(1)画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a09894a5af03a3d4b7d9d010e8876b.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a09894a5af03a3d4b7d9d010e8876b.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e93551ae5710954890b2a920893ca3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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8 . 已知集合
,
.
(1)若“
”是“
”的充分不必要条件,求实数
的取值范围;
(2)设命题
,
,若命题p为假命题,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871a4de3ee7603fcd0c5be1c5088dc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e6c537d678ea04d6c146b79bc14c6c.png)
(1)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba27566052abbb25340b6499ae3044a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ab0ccd3aee3d086dade99b619d49f6.png)
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解题方法
9 . 已知函数
是定义在
上的奇函数,且
.
(1)确定函数
的解析式;
(2)当
时,判断函数
的单调性,并证明;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bfd4c5e31782fdfcaae746dc56c65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad19d9b057bd7b2207dabe260e7bde86.png)
(1)确定函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab87accf1942ab80def96d12ef173163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94fa04b6bb348fa81dbbd0119677b07b.png)
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辽宁省营口市大石桥市第三高级中学2022-2023学年高一上学期期中数学试题辽宁省协作校2022-2023学年高一上学期期中考试数学试题江苏省宿迁市泗阳县实验高级中学2022-2023学年高一上学期期末数学试题(已下线)人教A版2019必修第一册(综合检测卷)-2022-2023学年高一数学必考点分类集训系列(人教A版2019必修第一册)江苏省镇江市扬中市第二高级中学2023-2024学年高三上学期阶段检测一数学试题(已下线)高一上学期期中数学试卷(基础篇)-举一反三系列(已下线)第3章 函数-【高中数学课堂】单元测试基础卷(人教B版2019)(已下线)专题2.2 函数的单调性、奇偶性、对称性与周期性【九大题型】
解题方法
10 . 已知
,
为常数,函数
.
(1)当
时,求关于
的不等式
的解集;
(2)对于给定的
,
,且
,
,证明:关于
的方程
在区间
内有一个实根;
(3)若
为偶函数,且
,设
,若对任意
,
均成立,求实数
的取值范围.
![](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/01ad38aec9b8b5c741a9e83943809967.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f359fbd7bb48389efebb8787398478a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)对于给定的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33890c6b0bf167514d44139d9dca0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7ecd5cee1dce002ba2356bc164c56b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803a468e5d66004e57372a5bf2c5e1b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35821eae71dfea3b136fe7ee19944a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3c81a19a9adcdb16b2327c77917166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b767854aade97dc70a9b32e99be19eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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