名校
解题方法
1 . 已知函数
.若存在非零常数
和非零常数
,对于集合
内的任意实数
,恒有
成立,则称
是
上的周期为
的
级类增周期函数;若存在非零常数
和非零常数
,对于集合
内的任意实数
,恒有
成立,则称
是
上的周期为
的
级类周期函数.
(1)设
,已知
是
上的周期为1的2级类增周期函数,求实数
的取值范围;
(2)已知
是
上的周期为1的
级类周期函数,且当
时,
.若函数
在
上严格增,求实数
的取值范围;
(3)已知
,设
.试问:是否存在
,使
是
上的周期为
的
级类周期函数?若存在,求出
和相应的
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd2119a78f42846475bcf8a2c7731c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0594ef5ddddd8c56c63eb42d26ef14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8bb96f6059e46592c5fb479fca0678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9e66b73038b6279d204a47a78902ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d31d07e0e178dd81de9ab409d9475e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859949479a010c5c7826c12cee16277e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2714d917db4de20fb9c3a2759b4d236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
解题方法
2 . 对于函数
,
和
,
,设
,若
,
,且
,皆有
成立,则称函数
与
“具有性质
”.
(1)判断函数
,
与
是否“具有性质
”,并说明理由;
(2)若函数
,
与
“具有性质
”,求
的取值范围;
(3)若函数
与
“具有性质
”,且函数
在区间
上存在两个零点
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02059edf02fba0e7c62b7c2a48ef1184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed7a0e7e7a3b49b4cd2e777a64e9061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573996f5d4b27434a4491928b59f301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e450d0e48276909b7387fb576df4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49636685bca80ed0864d65d829973f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798548b5fbb631a0828621581a741f06.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a151adfdf0446b1ac074bca90076df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba0154a5c65b0b304c7e4df2e738f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb8ca1f5da558af68ebe76d985dbbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b96ee0875a6bcaf9371fb9cfd7eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.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/04133adb6f1562d859510c9771b2e545.png)
您最近一年使用:0次
解题方法
3 . 已知
,函数
,若该函数存在最小值,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606ef9cb8c9c4f61ab2acc4c11fec693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e13117cac3eb310a36fe099e6471dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
是定义在
上的奇函数,且
时有
.
(1)写出函数
的单调区间(不要证明);
(2)解不等式
;
(3)求函数
在
,
上的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da3a6d011679952771607b3a166676b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f76cb639dc4ce8ed42b2c87cf93555b.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dd18467feea8eb478f4669a32c2d57.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65918d542354edf5a635765dbda36b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd486a0f19830239d7bf3a660f9d716.png)
您最近一年使用:0次
2024-01-23更新
|
143次组卷
|
3卷引用:上海市虹口区2019届高一第一学期期末考试数学试题
名校
解题方法
5 . 已知关于
的不等式
有实数解,则实数
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33514d9f49f7468ba13c04c88711d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-01-15更新
|
425次组卷
|
3卷引用:上海市松江区2023-2024学年高一上学期期末质量监控数学试卷
上海市松江区2023-2024学年高一上学期期末质量监控数学试卷 山东省临沂市沂水县第一中学2023-2024学年高一上学期期末模拟数学试题(二)(已下线)专题3 含绝对值的函数问题【讲】(压轴题大全)
6 . 定义:若
,则称
是函数
的
倍伸缩周期函数.设
,且
是
的2倍伸缩周期函数.若对于任意的
,都有
,则实数m的最大值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89bbd44f30ccc52f08aeff8a6566aa6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb52912a14ff077e0e2ae197d09da724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193832a691c3fe376bde9ba572c1268e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3618fe959a18bf1c64983581fc342bb.png)
您最近一年使用:0次
名校
解题方法
7 . 若存在实数
,对任意实数
,不等式
恒成立,则实数m的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad115150262742c809287560e2a4a794.png)
您最近一年使用:0次
2024-01-13更新
|
508次组卷
|
4卷引用:上海市建平中学2023-2024学年高一上学期期末数学试卷
上海市建平中学2023-2024学年高一上学期期末数学试卷上海市敬业中学2023-2024学年高二下学期5月月考数学试题(已下线)第10题 动静转换求范围,构造函数是关键(优质好题一题多解)(已下线)第11题 不等式里面含参数,转化与化归辟蹊径(优质好题一题多解)
名校
解题方法
8 . 已知
,其中
是常数,
.
(1)若函数
为奇函数,求实数
的值;
(2)若对任意实数
,均有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd870f1f669420f3c8caf96faec7cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2608a57caffde627dbf140ca22a2ff8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
9 . 已知函数
,其中
,记
,且函数
是偶函数.
(1)求函数
的表达式:
(2)若不等式
在区间
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43745e8daea75b38cab51bcea8026cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ea36101bd7f0cefa20125125903e0e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c335aadabdbf03c7125e4c90062e8b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabac9f69a121b9fe969c7b3fe721b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
10 . 如果函数
满足以下两个条件,我们就称
为
型函数.
①对任意的
,总有
;
② 当
时,总有
成立.
(1)记
,求证:
为
型函数;
(2)设
,记
,若
是
型函数,求
的取值范围;
(3)是否存在
型函数
满足:对于任意的
,都存在
,使得等式
成立?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
② 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdccde6a17dc78bec232630577f99d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d5873aa225a83805e1072ef8119b7a.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc540d6c4de05039557cdfe8c78ceeec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54428f4829c8061f79df9f492305c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951b05c96af4f7704de24ac541b3f172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb679de6747c1a9147225d7b61c436f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe0c952b97016a6816cfca66e024ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdc6e6a0e6584bea7deb91b0841fa28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe8e17429b079c4965fae3bef4e6b25.png)
您最近一年使用:0次
2024-01-10更新
|
408次组卷
|
2卷引用:上海市静安区2024届高三上学期期末教学质量调研数学试题