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1 . 已知定义在
上的函数
,若存在实数
,
,
使得
对任意的实数
恒成立,则称函数
为“
函数”;
(1)已知
,判断它是否为“
函数”;
(2)若函数
是“
函数”,当
,
,求
在
上的解.
(3)证明函数
为“
函数”并求所有符合条件的
、
、
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d637d748a2b196af6d91703881ae1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67758380edd3796902534cf0e52cb6a1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9697e701323f29c2b8fb4b69fdec2a50.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901a683d7456f2b2135bccb41e70e33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad324be3bebd9c8051c5f502df2b536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51870c1132971c292e4498255210546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4947f55ebd9b5438e46cb120d51be615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966055559e213bce8e92ef59ba03d2d4.png)
(3)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa79143526cf263a8fff8030446efa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67758380edd3796902534cf0e52cb6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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解题方法
2 . 已知定义在
上的函数
,集合
.
(1)若
,是否存在实数k,使得
,如果存在,求k;如果不存在,说明理由;
(2)若
,且当
时,
,求函数
在
的函数解析式;
(3)若
,是否存在一次函数
,使
,其中
,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279133c0f4a56f184329d132ad6357c8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4046c9f58f541732bd4d90b7719ba35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fa4434ffb809ce49a20db2aee573e4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d2c6a4bf4dd5296ec48b3cb961db00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19a14a9712f66204093b9dda61927b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f103a01fa039701e147e4b7e9353e999.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae92289c9645da9e330fee632aee99db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3062b19939118118a668ba074d14bbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b94fda0a88d994de1f73d1e37dc73ab.png)
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3 . 某科研小组对面积为8000平方米的某池塘里的一种生物的生长规律进行研究,一开始在此池塘投放了一定面积的该生物,观察实验得到该生物覆盖面积y(单位:平方米)与所经过月数
的下列数据:
为描述该生物覆盖面积y(单位:平方米)与经过的月数
的关系,现有以下三种函数模型供选择:
;
;
.
(1)试判断哪个函数模型更适合,并求出该模型的函数解析式;
(2)约经过几个月,此生物能覆盖整个池塘?
(3)经过4个月的研究掌握该生物生长规律后,科研小组需改善池塘生态,现有两种方案:
方案一:加入能抑制该生物生长的某种化学物质,使其覆盖面积y与经过的月数
的关系变为
;
方案二:在4月底集中打捞一次,使其覆盖面积减少到4平方米,生物增长速度不变.
问如何评价这两种方案,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001b45efc958ac178b5474919eab676e.png)
0 | 2 | 3 | 4 | |
4 | 25 | 62.5 | 156.25 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001b45efc958ac178b5474919eab676e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b8ef762b4e285a5f91dffde836ec2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b247af6ebd2d8654c11dbbf3b4d8e04e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
(1)试判断哪个函数模型更适合,并求出该模型的函数解析式;
(2)约经过几个月,此生物能覆盖整个池塘?
(3)经过4个月的研究掌握该生物生长规律后,科研小组需改善池塘生态,现有两种方案:
方案一:加入能抑制该生物生长的某种化学物质,使其覆盖面积y与经过的月数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fb89b2b9e548648bd5beb1bd460ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2960b9894617c0d423532c961f5978b2.png)
方案二:在4月底集中打捞一次,使其覆盖面积减少到4平方米,生物增长速度不变.
问如何评价这两种方案,并说明理由.
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解题方法
4 . 如图所示,AB为沿海岸的高速路,海岛上码头O离高速路最近点B的距离是120km,在距离B点300km的A处有一批药品要尽快送达海岛.现要用海陆联运的方式运送这批药品,设登船点C到B的距离为x,已知汽车速度为100km/h,快艇速度为50km/h.(参考数据:
.)
关于x的函数;
(2)当C选在何处时运输时间最短?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a7ff6bb8000946da9599d7d903ac9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
(2)当C选在何处时运输时间最短?
您最近一年使用:0次
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|
285次组卷
|
2卷引用:2024届上海市闵行(文绮)中学高考三模测试数学试卷
名校
5 . 将连续正整数1,2,3,
,
从小到大排列构成一个
,
为这个数的位数.例如:当
时,此时为123456789101112,共有15个数字,则
.现从这个数中随机取一个数字,
为恰好取到0的概率.
(1)求
;
(2)当
时,求
得表达式;
(3)令
为这个数中数字0的个数,
为这个数中数字9的个数,
,
,求当
时,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4673710cd589e1b6cd3d2906e36791df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df313df25c54af0180e52424f480260b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081fad2749f3f201cf2c324c3d0dd190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadc4f26938f7a9d55006ab4d3c1e102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6df056ae0ceeac78f539e23aadd6fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6291d7b91f71daa0b3c4fa02dc7a5ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eaaa90099b6eb96a5730619ca2df08f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e464598d8d334b4d5a01c25f7ef9021c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081fad2749f3f201cf2c324c3d0dd190.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d85d20b743e236a83edb22d5229d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13d06dcfd70149e4f495614f36b3a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44b482719577dde6fa146e44aa0c448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6291d7b91f71daa0b3c4fa02dc7a5ea.png)
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解题方法
6 . 已知函数
,
,
.
(1)求
的解析式;
(2)已知函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数,据此结论求函数
图象的对称中心;
(3)设函数
,
,若对任意
,
恒成立,求m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba465fbf4fac6458f705485ae6315f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ee5f43412795671704ab0e8d0b2f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec65a2bec3d4296c613a80b3ae41d5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35499c5e106e867c251bca59fb95bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4583392576aebb3c614e449e5137f702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7b15902fd2f3a22c2acea407fbe0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad1767ddada26f61696862e85a8b858.png)
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2023-02-21更新
|
322次组卷
|
4卷引用:第五章 函数的概念、性质及应用(单元重点综合测试)-单元速记·巧练(沪教版2020必修第一册)
(已下线)第五章 函数的概念、性质及应用(单元重点综合测试)-单元速记·巧练(沪教版2020必修第一册)(已下线)第五章 函数的概念、性质及应用(压轴题专练)-单元速记·巧练(沪教版2020必修第一册)山东省青岛市西海岸新区2022-2023学年高一下学期调研检测(分科考试)数学试题山东省青岛市2022-2023学年高一上学期调研检测数学试题
名校
解题方法
7 . 设
是一个定义域为
的函数.若
是
的一个非空子集,且对于任意的
,都有
,则称
是
关联的.
(1)判断函数
和函数
是否是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6535346c47957c14aa0987f66ad25d04.png)
关联的,无需说明理由.(
表示不超过
的最大整数)
(2)若函数
是
关联的,且在
上,
,解不等式
.
(3)已知正实数
满足
,且函数
是
关联的,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084df0babb739a54a118e5a1b6800891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0590061eec8dc72a825b9bd309912c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da6f7c4470c8478d7c7cf1911fe375f.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e3204e4dc47a448860779349efcedf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6535346c47957c14aa0987f66ad25d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ab85825d4a002600ca41bd3cd2ee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77304f8a896285017e8ba2d9d5bc8d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa774d7d80401d380a9f6b63112d4a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974296ff9c97484ef099a11d3dd23ff9.png)
(3)已知正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b570b802d338d0d906c73fffe1a2a45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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8 . 已知定义域为
的函数
满足:①对
,恒有
;②当
时,
.
(1)求
的值;
(2)求出当
,
时的函数解析式;
(3)求出方程
在
中所有解的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe896777dc4f9aebb0e6b11ed3ed37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b8e9bb1e11d02cc2190a6e5ede4293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b96c2c79f7d0a248ed590a0bce7eb8bd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a53e132781c63d215c6c2cee3d306.png)
(2)求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538190cf2a2e6f248188ae111a162ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf910f82c3094b267a3d481d23d829f.png)
(3)求出方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf81798e77ead893922361d5e1d4548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5cf57d2484a1293cfd296a5ae2da1e.png)
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9 . 已知函数
,
,如果对于定义域D内的任意实数x,对于给定的非零常数P,总存在非零常数T,恒有
成立,则称函数
是D上的P级递减周期函数,周期为T;若恒有
成立,则称函数
是D上的P级周期函数,周期为T.
(1)判断函数
是R上的周期为1的2级递减周期函数吗,并说明理由?
(2)已知
,
是
上的P级周期函数,且
是
上的严格增函数,当
时,
.求当
时,函数
的解析式,并求实数P的取值范围;
(3)是否存在非零实数k,使函数
是R上的周期为T的T级周期函数?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99d26e65e02ba8ec1b10529e5a0253c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab21d3bab25b356abae92e6ff08f7d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499f8a6c1737ed4c552a93b0b64e4958.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac920b4fb011075ccd75d7807cca5a26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2645398c3946e1a9282c219824f167d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc079255ea327cb71b3bcfe48693d17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37475d9dc070faa59a1801b59d2ec2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)是否存在非零实数k,使函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a3ca0dd34a3cd5ca9a5c5055ceee23.png)
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2022-04-26更新
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10卷引用:上海市闵行区(闵行中学、文绮中学)2021-2022学年高一下学期期中数学试题
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名校
解题方法
10 . 已知定义在R上的函数
满足:
在区间
上是严格增函数,且其在区间
上的图像关于直线
成轴对称.
(1)求证:当
时,
;
(2)若对任意给定的实数x,总有
,解不等式
;
(3)若
是R上的奇函数,且对任意给定的实数x,总有
,求
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ee081ef6ed3261541eade37f4f9da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ee081ef6ed3261541eade37f4f9da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea438617b79dcfca03dacdf20929046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(2)若对任意给定的实数x,总有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e298fe246eef819dd9b1edabe3bb9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cbbf4d5b8ecbfccc5de39781396d07.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b762ca4a3a079282f7c2cdfc5d39f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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