名校
解题方法
1 . 若
是定义在
上的增函数,其中
,存在函数
,
,且函数
图像上存在两点
,
图像上存在两点
,其中
两点横坐标相等,
两点横坐标相等,且
,则称
在
上可以对
进行“
型平行追逐”,即
是
在
上的“
型平行追逐函数”. 已知
是定义在
上的奇函数,
是定义在
上的偶函数.
(1)求满足
的
的值;
(2)设函数
,若不等式
对任意的
恒成立,求实数
的取值范围;
(3)若函数
是
在
上的“
型平行追逐函数”,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3df718662452f53034b6f702e46dcdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958a7330503a10fecf9b6b6f4a30ea8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5ffb9d0b5dc940f53d7370419a08db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c33c52de7a2c9d148e44283eec3dbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdeb8cfadb41d94aaa1ba534aa040dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e257d683ceaca6c6c3ee5ada0e447b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d908675a3ce0661cf6b3d7823143d4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb874a24bc2fa3d232070f16712aa05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86df4f1b31c51da3551a76606d553f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bb6dbc79a74521af6338b0140b713b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86644d5b1157b35cf7b825f108d4c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
23-24高一下·全国·课后作业
解题方法
2 . 结合生活经验和其他学科的知识,举出三个周期函数的实例.
您最近一年使用:0次
24-25高一上·全国·课后作业
3 . 初中学过哪些类型的函数?那时是怎样认识函数单调性的?经历了高中函数的研究,你对函数单调性有什么新的理解?
您最近一年使用:0次
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82a8a3968ec0509bf3c338a939fb07.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/fa614b5d-38d8-419e-b9bc-3c58f1ef717a.png?resizew=173)
(1)完成下列表格,并在坐标系中描点画出函数
的简图;
(2)根据(1)的结果,若
(
),试猜想
的值,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82a8a3968ec0509bf3c338a939fb07.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/fa614b5d-38d8-419e-b9bc-3c58f1ef717a.png?resizew=173)
(1)完成下列表格,并在坐标系中描点画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d82a8a3968ec0509bf3c338a939fb07.png)
(2)根据(1)的结果,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
1 | 2 | 4 | |||
您最近一年使用:0次
名校
解题方法
5 . 已知函数
为偶函数,函数
为奇函数,
对任意实数
恒成立.
(1)计算
、
的值;
(2)试探究
与
的关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76262040490d4b828bd34766db081c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7c57efb5fb91b158e641da042c9b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9eed8d517d8c331ed34319521a5912.png)
(2)试探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a917e05cfca420bd81408cc7a02133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
解题方法
6 . 已知幂函数
,
(1)求
的值;
(2)若_________写出函数
的单调区间(不需证明单调性),并利用
的单调性解不等式
.
①函数
为奇函数;②函数
为偶函数,从这两个条件中任选一个填入横线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b785be7d800df095d215cfda2b2ad8c8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若_________写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2212fb0e316382c889cc409d3259afce.png)
①函数
![](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
7 . 随着人工智能的飞速进展,临港某车辆装配车间每2小时装配完成一辆车.按照计划,该车间今天生产8小时.从当天开始生产的时刻起,所经过的时间x(单位:小时)与装配完成的车辆数
(单位:辆),表示为函数
.
(1)用分段表示法写出函数
的解析式;
(2)数学上,常用
表示不大于
的最大整数,例如
,
;
也叫做取整函数.请用取整函数写出函数
的简洁表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)用分段表示法写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)数学上,常用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b1ef02e27ed5c065c42a0de0a88199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2083b5aa3f5e29a502c09487dde8db16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7179c645736d68c90023f83d7f11ed01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
名校
8 . 分别根据下列两个实际背景
(1)求函数
的解析式;
(2)画出函数
的图象;
(3)求函数
的值域.
背景1:在国内投递外埠平信,每封信不超过
付邮资80分,超过
不超过
付邮资160分,超过
不超过
付邮资240,依此类推,每
的信应付邮资
(单位:分).
背景2:如图所示,在边长为2的正方形
的边上有一个动点
,从点
出发沿折线.
移动一周后,回到
点.设点
移动的路程为
,
的面积为
.
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
背景1:在国内投递外埠平信,每封信不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0771acf9b0116e83a098817e8cf588e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0771acf9b0116e83a098817e8cf588e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55c922dcbe2ca3c2557f997281fcd24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55c922dcbe2ca3c2557f997281fcd24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45cf1e9fd0d9a95b28098cee9b398f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de77d3c5ee5d9c7f06f332d8dd79288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
背景2:如图所示,在边长为2的正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/9d7392ba-079c-43f4-96fd-ca7604c8b858.png?resizew=149)
您最近一年使用:0次
9 . 医院通过撒某种药物对病房进行消毒,已知开始撒放这种药物时,浓度激增,中间有一段时间,药物的浓度保持在一个理想状态,随后药物浓度开始下降.若撒放药物后3小时内的浓度变化可用下面的函数表示,其中x表示时间(单位:小时),
表示药物的浓度:
.
(1)撒放药物多少小时后,药物的浓度最高?能维持多长时间?
(2)若需要药物浓度在41.75以上消毒1.5小时,那么在撒放药物后,能否达到消毒要求?并简要说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebc1ee5ba8cbab8b469f25c43bb4cf7.png)
(1)撒放药物多少小时后,药物的浓度最高?能维持多长时间?
(2)若需要药物浓度在41.75以上消毒1.5小时,那么在撒放药物后,能否达到消毒要求?并简要说明理由.
您最近一年使用:0次
解题方法
10 . 三叉戟是希腊神话中海神波塞冬的武器,而函数
的图象恰如其形,因而得名三叉戟函数,因为牛顿最早研究了这个函数的图象,所以也称它为牛顿三叉戟.已知函数
的图象经过点
,且
.
(1)求函数
的解析式;
(2)用定义法证明:
在
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9cc876a2a8d1461b737861169248ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9cc876a2a8d1461b737861169248ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9275848b5c91230c249a45f1bfc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2635c6e599f816c706e471a3c197d5.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)用定义法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
您最近一年使用:0次