解题方法
1 . 设
(a为实常数),
与
的图像关于y轴对称.
(1)若函数
为奇函数,求a的取值;
(2)当a=0时,若关于x的方程
有两个不等实根,求m的范围;
(3)当|a|<1时,求方程
的实数根个数,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b9b42638033a93f26cbf4fd89b76ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae905f856b26183ebe83225350df5a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110c8d90cd5808b83431c72cdb1976e0.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495d1f17eec7fe720a8fd8840822f55e.png)
(2)当a=0时,若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9405eb72b163ac2b712231899fe398d.png)
(3)当|a|<1时,求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4603bbe40ed845c0fba5dea69053d305.png)
您最近一年使用:0次
23-24高一上·上海浦东新·阶段练习
名校
2 . 已知函数
(
,常数
).
(1)求函数
的零点;
(2)根据
的不同取值,判断函数
的奇偶性,并说明理由;
(3)若函数
在
上单调递减,求实数
的取值范围,证明函数
在
上有且仅有1个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14a2156c6690b324f7929b3b3553970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)根据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f0be268c091289f25b2d4cb9f8f789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
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名校
解题方法
3 . 已知函数
在区间
上是单调函数
(1)求实数m的所有取值组成的集合
;
(2)试写出
在区间
上的最大值
;
(3)设
,令
,对任意
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8546e90cc8a674a6ac35ada6d94077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
(1)求实数m的所有取值组成的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b35198b079edaa66c4ee701f9a2964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7879c53f7ae6a41a900c9bf630c30f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930995172d12e12d8173aec823f1982b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5eb1e81ec6f44e4cb59ce214b949a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-12-03更新
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2卷引用:湖北省恩施市第一中学2022-2023学年高一上学期12月月考数学试题
名校
4 . 已知
,
,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae9f908aabcd9d9c46a0ecdfd1d6c12.png)
(1)求
的周期和单调递减区间;
(2)设
为常数,若
在区间
上是增函数,求
的取值范围;
(3)设
定义域为
,若对任意
,
,不等式
恒成立,求实数
的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbb45d951aa4c64d07ea0e9394f2df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1dfdb520f2dd637ccb5606d4695823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae9f908aabcd9d9c46a0ecdfd1d6c12.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e665ca2220e4b27b78a173ff756e1eda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4607e9f81a317703cf52ef9dfe685c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce53b7483eef4f0fb3334107acc4e1de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbd17006e2625ff6748f6d098ea6573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841a7b00bf7477dff488ec7bbe9d8ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-07-15更新
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7卷引用:江西省赣州市赣县第三中学2022-2023学年高一上学期10月月考数学(理)试题
江西省赣州市赣县第三中学2022-2023学年高一上学期10月月考数学(理)试题甘肃省白银市靖远县第四中学2022-2023学年高一下学期6月月考数学试题贵州省遵义市2021-2022学年高一下学期期末质量监测数学试题贵州省遵义市2021-2022学年高一下学期期末质量监测数学试题四川省仁寿第一中学校南校区2022-2023学年高一下学期期中考试数学试题 (已下线)高一下学期期末真题精选(压轴60题20个考点专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)(已下线)上海市高一下学期期末真题必刷04-期末考点大串讲(沪教版2020必修二)
5 . 设
,函数
.
(1)若
,判断并证明函数
的单调性;
(2)若
,函数
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
上的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f8ca3916770d199f7edd59b1722a86.png)
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27b285c7ddbb366a8f1a183e2194ac1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475963eea170ff0bbdaf2f0b706dfc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f8ca3916770d199f7edd59b1722a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06038810f4b137ab903256336b433b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
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2022-01-21更新
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2卷引用:浙江省湖州市南浔高级中学2023-2024学年高一下学期第一次月考数学试卷
名校
6 . 设
,函数
.
(1)若
,判断并证明函数
的单调性;
(2)若
,函数
在区间
(
)上的取值范围是
(
),求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5029bd373d0a619fd342eeb67a03dd2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f8ca3916770d199f7edd59b1722a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b97b295f88972ba1c7e3cefda0885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
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2022-02-16更新
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4卷引用:四川省宜宾市叙州区第一中学校2022-2023学年高一上学期第三学月考试数学试题
7 . 已知函数
.
(1)根据a的不同取值,判断函数
的奇偶性(只写结论,不需证明);
(2)设函数
,当
时,对于
,总有
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ac7df0685ba0947428ad4b7f99622a.png)
(1)根据a的不同取值,判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22382e94f33493220314c2a5ace3b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ccb51adec8cde167e2198ada879e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb184f810b48f7dcda528c76acf33ab.png)
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名校
解题方法
8 . 定义两类新函数:
①若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使得
成立,则称该函数为“
函数”;
②若函数
对定义域内的每一个值
,在其定义域内都存在唯一的
,使得
成立,则称该函数为“
函数”.
(1)设函数
的定义域为
,已知
是某一类新函数,试判断
是“
函数”还是“
函数”(不需说明理由),并求此时
的范围;
(2)已知函数
在定义域
上为“
函数”,若存在实数
,使得对任意的
,不等式
都成立,求实数
的取值范围.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c411a8fd18c8de5c7de91ead2534602b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a83c952b58c39be1b0d43d304e0911.png)
②若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c98c995fc2687a803998d262d754e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da9ea25accbf7eeb60424224b68c092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a83c952b58c39be1b0d43d304e0911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c918ca5d4e6d46ed130f85e5fa608d.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53275eb34d75ead1b48d1d78123d536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56002ab09438fcb642fde70b10ee9720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdf896f6685774c416482a887484fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94526b73a995b128c50c2487e192f057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
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2020-08-07更新
|
594次组卷
|
2卷引用:安徽省合肥市第六中学2019-2020学年高一下学期学情检测数学试题
9 . 已知二次函数
满足下列3个条件:
①
的图象过坐标原点;②对于任意
都有
;③对于任意
都有
.
(1)求函数
的解析式;
(2)令
.(其中m为参数)
①求函数
的单调区间;
②设
,函数
在区间
上既有最大值又有最小值,请写出实数p,q的取值范围.(用m表示出p,q范围即可,不需要过程)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cbf67f0605a8d1f4499b156785001f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b129a86f37fbbdf5a5808f13924e819f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b45f20b8f07836bb5d9941ae862233.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e257b2b02bcd57c116841807979bbc.png)
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2020-01-04更新
|
393次组卷
|
3卷引用:江苏省盐城市东台三仓中学2019-2020学年高一上学期12月月考数学试题
10 . 已知
,
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d671628856390127cbffd2f8bd098e.png)
(1)当
时,请写出
的单调递减区间;
(2)当
时,设
对应的自变量取值区间的长度为l(闭区间
的长度定义为
)求l关于a的表达式,并求出l的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43be8655375defb2d244844cbba59ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55b6ea77ab1bb966da0ca0e73b97dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d671628856390127cbffd2f8bd098e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a59011b33c66ca24e0fed4243b8e704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e669d502287cab6a74d72fb4aa1ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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