名校
1 . 在研究函数过程中,经常会週到一类形如
为实常数且
的函数,我们称为一次型分式函数.请根据条件完成下列问题.
(1)设
是实数,函数
,请根据
的不同取值,讨论函数
的奇偶性,并说明理由;
(2)设
是实数,函数
.若
成立的一个充分非必要条件是
,求
的取值范围;
(3)设
是实数,函数
,若存在区间
,使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9796db5f297d4023eac8d1aa4739c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b744e7cd7496125a9bcd6b756d09ebff.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1944af8ede16275cdcbe721a81870d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8aade587301e484fe76bdf87e6d5b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47f8d234c1df11e957b9bd7d3f2da47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe2a076aa933bf55763c67b8734b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af24aeacd2576456cc192826ecd5b107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcc3c97c6d73f7ef44b90ec6f3065ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2 . 不等式
对满足
的一切实数m的取值都成立,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc7775323a072962cd51fba2d6569a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6bd21a21a429c595ca5b1d94b567be.png)
您最近一年使用:0次
名校
3 . 设
,函数
.
(1)若
,求证:函数
为奇函数;
(2)若
,判断并证明函数
的单调性;
(3)若
,函数
在区间
上的取值范围是
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6fe56c70ed96e7f0ee48063dae9fc7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)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/98e6fca71fccb890f3ad8501ea4f560e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d42f621464019a86fadf05723784e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2023-03-14更新
|
644次组卷
|
3卷引用:湖南省岳阳市岳阳县第一中学2023-2024学年高一下学期3月月考数学试题
名校
解题方法
4 . 已知函数
若
的值域为R,则a的一个取值为____________ ;若
是R上的增函数,则实数a的取值范围是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e372ebb8eae888f8db06520d6fc4316d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
5 . 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)
您最近一年使用:0次
2022-07-15更新
|
1649次组卷
|
7卷引用: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)
(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)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 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(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)
6 . 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)
您最近一年使用:0次
2022-01-21更新
|
674次组卷
|
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
7 . 意大利画家列奥纳多·达·芬奇曾提出:固定项链的两端,使其在重力的作用下自然下垂,项链所形成的曲线是什么?这就是著名的“悬链线问题”,后人给出了悬链线的函数表达式
,其中
为悬链线系数,
称为双曲余弦函数,其函数表达式
,相反地,双曲正弦函数的函数表达式为
.
(1)证明:①
;
②
.
(2)求不等式:
的解集.
(3)已知函数
存在三个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65623d246ccde18e941c9bda7011ef65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ff88c570435584c4df32454224c442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0639494fc8cc7a048c7621f972eae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a59c8dc71935b342d42cb4a54eed27.png)
(1)证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec3182982e6dcf905ea35d6b5be5f48.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe43cb3653c29dd797074b27780695a9.png)
(2)求不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf091e70e33483f99554568eb54a10a.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f307ed8ec3f398d3d3e445266396acdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)求不等式
的解集;
(2)
,将
的图象向右平移
个单位后得到函数
.若对任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcaf2bf2e03dd6d33e03b69c5a318b90.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195a523f1aa349541bb5b846bcc594dd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc5c3594ca8db401fbfdc7ddb57b13c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667466e8b8b971a8ea50cd080501577e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a777674bdd16996988b6ba37de5c6142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-05-08更新
|
309次组卷
|
2卷引用:广东省河源市部分学校2023-2024学年高一下学期5月期中联考数学试题
名校
9 . 已知函数
.
(1)求不等式
的解集;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d638517c0728b6785bee04e6b682b18.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5173999625baf17bc6a22b9ed99673e4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136f4ce88d0dd0cb8b9ff315cb866e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-04-12更新
|
193次组卷
|
2卷引用:华大新高考联盟2024届高三4月教学质量测评文科数学试题(老教材全国卷)
2024·全国·模拟预测
解题方法
10 . 设函数
.
(1)求
的解集;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e879a49d41728d578bac40deb1f1ddc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f92fe4b4ba8a3348ed6d051d1bee0a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次