名校
解题方法
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
成立,则称该函数为“依赖函数”.
(1)判断函数
是否为“依赖函数”,并说明理由;
(2)若函数
在定义域
(
)上为“依赖函数”,求
的取值范围;
(3)已知函数
在定义域
上为“依赖函数”.若存在实数
,使得对任意的
,不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.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/4920f64bf2d21782d3cc1dcf762a82b6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5104d5cb070f4821eed3e4b6d4444312.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067a7039d0a209dde7ee2ab83f165cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd8466b576ad34d6ef492599940f4b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f537c893dfe2661ba4273cf218c72d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ed0b4f5d3f3692248103c019dfc7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a62181e63e71982641232f19bd3b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ae0f4860c40e7f07da441d7a082c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39106d1bdd098fc71c68b9c606891eeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6cfdec5cc7be35e031e3ff6e13f38d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
您最近一年使用:0次
2024-03-01更新
|
332次组卷
|
2卷引用:广东省深圳市福田区红岭中学2023-2024学年高一下学期第一次月考数学试卷
2 . 已知函数
.
(1)判断函数
的奇偶性,并说明理由;
(2)讨论函数
在
上的单调性,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5f5490b9d6b025c720fae613a26e35.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
您最近一年使用:0次
2024-02-24更新
|
309次组卷
|
2卷引用:广东省广州市越秀区2023-2024学年高一上学期期末数学试题
3 . 已知函数
在区间
上的最小值为
.
(1)求常数
的值;
(2)将函数
向右平移
个单位,再向下平移
个单位,得到函数
,请求出函数
,
的单调递减区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ef71756ef8bfae1442a859d0a60392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c1547d887b29e39542997731a5288b.png)
您最近一年使用:0次
解题方法
4 . 已知
是定义在
上的奇函数.
(1)求
的解析式;
(2)已知
,若对于任意
,存在
,使得
成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7686198477e82befeebe163c8f521ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdf7c8f771c4605d81e519e13c6dc87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0984867afe93021a6917f32694ae1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05af9933e2e059567ce364975b601b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)若
,求实数
的值,并求此时函数
的最小值;
(2)若
为偶函数,求实数
的值;
(3)若
在
上是减函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bbf7921a8df97507fe1c864e9e91ad.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6855784817151468771f29c0fc38fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e38dcae548c14616215bc6f97166229.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
6 . 美国对中国芯片的技术封锁,激发了中国“芯”的研究热潮.某公司研发的
两种芯片都已经获得成功.该公司研发芯片已经耗费资金2亿元,现在准备投入资金进行生产.经市场调查与预测,生产
芯片的毛收入与投入的资金成正比,已知每投入1亿元,公司获得毛收入0.25亿元;生产
芯片的毛收入
(亿元)与投入的资金
(亿元)的函数关系为
,其图像如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/7309e76c-288e-46fd-aab9-da1d191c417d.png?resizew=194)
(1)试分别求出生产
,
两种芯片的毛收入
(亿元)与投入的资金
(亿元)的函数关系式;
(2)如果公司只生产一种芯片,生产哪种芯片毛收入更大?
(3)现在公司准备投入
亿元资金同时生产
,
两种芯片.设投入
亿元生产
芯片,用
表示公司所获利润. 当
最少为多少时,公司才不亏本.(不亏本指利润不小于0)
(利润
芯片毛收入
芯片毛收入-发耗费资金)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01978310b39dd1a60754ce8abf61d14c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/7309e76c-288e-46fd-aab9-da1d191c417d.png?resizew=194)
(1)试分别求出生产
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)如果公司只生产一种芯片,生产哪种芯片毛收入更大?
(3)现在公司准备投入
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(利润
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6219f0c257aaecd6efb927710c132b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8d20bc7af01e5f57036613d19447b0.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)诺
为偶函数,求
的值;
(2)若
为奇函数,求
的值;
(3)在(2)的情况下,若关于
的不等式
在
上恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84a452b5bc7705e5ac83155f1990cd0.png)
(1)诺
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)在(2)的情况下,若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7853190eac5b25819a86097bdfea8c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-02-18更新
|
325次组卷
|
2卷引用:广东省茂名市高州市石鼓中学2023-2024学年高一下学期第一次校际联考数学试卷
名校
解题方法
8 . 已知
,
.
(1)若
,判断
的奇偶性.
(2)若
是单调递增函数,求
的取值范围.
(3)若
在
上的最小值是3,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87ecbabf349ed188fb1dcee2a4c8a24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec90f93919eb1d1a6b0ed9d05bf91c02.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9099a75c433e97bbe05052a00110571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
9 . 已知
,函数
.
(1)若
,求
的最小正周期和单调区间:
(2)若
的最大值是
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3fa587a9b2e1c9fe82750db0ec22fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdbcb4dc66a5e598aa5cf3e49ff8987.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce0dc28340738e090bd10d6d675d8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
您最近一年使用:0次
解题方法
10 . 已知函数
(
,且
).
(1)若函数
的图象过
和
两点,求
的解析式;
(2)若函数
在区间
上的最大值比最小值大
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a33dc3326e335a7e519b86093a53fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1946e3d90d953d30a8cce367b06c394e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9eddc0732dffa8a715a6fb92da64cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a248e47163191168a1b363937eebd618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6322308be685c4a21efa285279afa9e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次