名校
1 . 已知函数
.
(1)求
的单调递减区间;
(2)若函数
与
的最大值相同,最小值相同,单调递增区间相同,求
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc50b8e1cc267f0becf72803dde7e3ab.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad3d9ef4dd0c0f0474cb7a25293fc6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172723002461ae60798317e2f10f6c2.png)
您最近一年使用:0次
2 . 已知函数
.
(1)若
,且
图象关于
对称,求实数
的值;
(2)若
,
(i)方程
恰有一个实根,求实数
的取值范围;
(ii)设
,若对任意
,当
时,满足
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb49512c66fdf46280daa506f5458004.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be033199f77a8822a8514eafab5162d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f59eb2942c435d69c1e48c2c61c111.png)
(i)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e735656890d668f67f1538fe702b366a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc373640d8d66865998853b3c3f7be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71530343bd5d7121c2e77b10aff7bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57318f5659bc916624d975b7146e8a4.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
3 . 函数
的图象关于坐标原点成中心对称的充要条件是函数
为奇函数,可以将其推广为:函数
的图象关于点
成中心对称的充要条件是函数
为
关于
的奇函数,给定函数
,关于
中心对称.
(1)求
的值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
,若对任意的
,总存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291aaad429837ab6dc1f99b9f7327cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f4cf449b51f221f9cb26e71a9dbebb.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/0a42e14c5d826813dd33e04be2d2c26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f5fc756bf1aa3099dba53a6caba5a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9dccd1d5763d4c2a8799ead64f475d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee1e47231d0c468d7e2d720a0fdeee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1247c1725b0a2037e53cbf5f7a668483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af9f0245165190c43c12ab642a97a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
4 . 设函数
,关于
的一元二次不等式
的解集为
.
(1)求不等式
的解集;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc844e0e11ada7c71210c5ab80a47e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2157b41548f02a86a438e63238719841.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765f521fa075140051199a3e1908fa91.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad037a2985b51525ccb9fc0253f2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
5 . 设
为给定的实常数,若函数
在其定义域内存在实数
,使得
成立,则称函数
为“
函数”.
(1)若函数
为“
函数”,求实数
的值;
(2)证明:函数
为“
函数”;
(3)若函数
为“
函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bb27ea04432576f9fa34d6fc0bd971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d5408842cf8095d3b0a4e1bef10226.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0a00c98a1184c0a8f3a92610bd306b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d9232cc485aadda3d0c529eee4616f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efab890e2314c6fbebebe6341fb7879a.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65f9fdfab6e5485d35bdfe7d1909c257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efab890e2314c6fbebebe6341fb7879a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
6 . 对于函数
,
为函数定义域,若存在正常数
,使得对任意的
,都有
成立,我们称函数
为“
同比不增函数”.
(1)若函数
是“
同比不增函数”,求
的取值范围;
(2)是否存在正常数
,使得函数
为“
同比不增函数”,若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f69a10dd74a5189353a5db9d5828ac3.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/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f7f1ed660ed810ad4ffd5d0a6d3762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03cddfaa4522ab14daa358d2d5af019e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)是否存在正常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f44b70df66b4e8b1f958d1335fb83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
名校
7 . 为了丰富市民业余生活,推进美丽阜阳建设,市政府计划将一圆心角为
,半径为
米的扇形
空地
如图
改造为市民休闲中心,休闲中心由活动场地和绿地两部分组成,其中活动场地是扇形的内接矩形,其余部分作为绿地,城建部门给出以下两种方案:
方案
让矩形的一个端点位于
上,其余端点位于
,
上.
方案
让矩形的两个端点位于
上,其余端点位于
,
上.
请你先选择一种方案,并根据此方案求出活动场地面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821b8672d030c240ff230a0174aa7a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
方案
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a34029cc0f7665d32694f0837b2f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
方案
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508f5b0a8b1ac58f88d886a850f3ae1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
请你先选择一种方案,并根据此方案求出活动场地面积的最大值.
您最近一年使用:0次
8 . 设函数
,已知函数
的图象经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527edc20697fffcb63c8ac7ada531f86.png)
(1)求函数
的解析式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)求函数
在
上的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1775d0be2d768caaa2f59f6b15128603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527edc20697fffcb63c8ac7ada531f86.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579537c2483ebf9638830b54a7b714b2.png)
您最近一年使用:0次
2024-02-21更新
|
518次组卷
|
2卷引用:安徽省阜阳市第三中学2023-2024学年高一上学期期末考试数学试题
名校
解题方法
9 . (1)计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f789027ef00d99097ee55d2285a53a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f789027ef00d99097ee55d2285a53a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33511b01d9202e3c7b6ee2fe868dd223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f19975d8734bcd043c74ff51886d88b.png)
您最近一年使用:0次
10 . 已知函数
是定义在
上的奇函数.
(1)求
和实数b的值;
(2)若
满足
,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24e25e2fc13d912ae6be04fe4103ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e91676c7adfd65a76f56a0c1d4bbe0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e5ec00cb05327200b7919d15309377.png)
您最近一年使用:0次