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上海市2018-2019学年上海中学高三上学期数学周练

一. 填空题

1. 函数22()log (34)f x x x =--的定义域为

2. 已知函数13()f x x =，[8,64]x ∈的值域为A ，集合2{|430}B x x x =-+<，则A B =

3. 函数2()1log f x x =+与()y g x =的图像关于直线y x =-对称，则(3)g =

4. 函数()f x 满足(4)()f x f x +=（x ∈R ），且在区间(2,2]-上， cos 022()1||202x x f x x x π?<≤??=??+-<≤??

，则((15))f f 的值为 5. 设()f x 是定义在R 上以2为周期的偶函数，已知(0,1)x ∈，12

()log (1)f x x =-，则函

数()f x 在(1,2)上的解析式()f x =

6. 已知函数2()(1)1f x ax b x b =+++-，若对任意的b ∈R ，函数()()F x f x x =-总有两个不同的零点，则a 的取值范围为

7. 能说明“若(1)()f x f x +>对任意的x ∈R 都成立，则()f x 在R 上是增函数”为假命题的一个函数是

8. 已知函数2||()24x x m f x x mx m x m ≤?

=?-+>?，其中0m >，若存在实数b ，使得关于x 的方程()f x b =有三个不同的根，则m 的取值范围为

9. 已知函数2

(21)()12x x f x x

+=+在区间[2018,0)(0,2018]-上的最大值为M ，最小值为 N ，则M N +=

10. 设()f x 是定义在R 上且周期为1的函数，在区间[0,1)上，2()x x D f x x x D ?∈=???

，其中集合*1{|,}n D x x n n

-==∈N ，则方程()lg 0f x x -=的解的个数是 11. 函数()y f x =的定义域为[1,0)(0,1]-，其图像上任一点(,)P x y 满足221x y +=， ① 函数()y f x =一定是偶函数；② 函数()y f x =可能既不是偶函数，也不是奇函数； ③ 函数()y f x =可以是奇函数；④ 函数()y f x =如果是偶函数，则值域是[0,1)或(1,0]-； ⑤ 函数()y f x =值域是(1,1)-，则()y f x =一定是奇函数；

其中正确命题的序号是（填上所有正确的序号）

12. 已知函数()f x 满足对任意的实数x 、y ，均有()()()6f x y f x f y xy +=++，且

(1)(1)9f f -≥，则2()3

f =

二. 选择题

13. “1a >”是“函数()2x f x a =-（0a >且1a ≠）在区间(0,)+∞上存在零点”的（）

A. 充分不必要条件

B. 必要不充分条件

C. 充要条件

D. 既不充分也不必要条件

14. 若函数()f x （x ∈R ）满足(1)f x -+、(1)f x +均为奇函数，则下列结论正确的是（）

A. ()f x -为奇函数

B. ()f x -为偶函数

C. (3)f x +为奇函数

D. (3)f x +为偶函数

15. 已知函数()f x （x ∈R ）满足()2()f x f x -=-，若函数1x y x

与()y f x =图像的交点为11(,)x y ，22(,)x y ，???，(,)m m x y ，则1

()m i i

i x y =+=∑（） A. 0 B. m C. 2m D. 4m

16. 如果函数()y f x =图像上任意一点的坐标(,)x y 都满足方程lg()lg lg x y x y +=+，那么正确的选项是（）

A. ()f x 是(0,)+∞上的减函数，且4x y +≤

B. ()f x 是(1,)+∞上的增函数，且4x y +≥

C. ()f x 是(1,)+∞上的减函数，且4x y +≥

D. ()f x 是(1,)+∞上的减函数，且4x y +≤

三. 解答题

17. 如图，灌溉渠的横断面是等腰梯形，底宽及两边坡总长度为l ，边坡的倾斜角为60°.

（1）求横断面面积y 与底宽x 的函数关系式；

（2）已知底宽[,]42

l l x ∈，求横断面面积y 的最大值和最小值.

18. 已知函数2()log (424)x x f x b =+?+，()g x x =.

（1）当5b =-时，求()f x 的定义域；（2）若()()f x g x >恒成立，求b 的取值范围.

19. 设函数()()||f x x a x b =-+.

（1）当2a =，3b =时，画出函数()f x 的图像，并求出函数()y f x =的零点；

（2）设2b =-，且对任意[1,1]x ∈-，()0f x <恒成立，求实数a 的取值范围.

20. 已知3a ≥，函数2()min{2|1|,242}F x x x ax a =--+-，其中min{,}p p q p q q p q

≤?=?

>?. （1）求使得等式2()242F x x ax a =-+-成立的x 的取值范围；

（2）① 求()F x 的最小值()m a ；② 求()F x 在区间[0,6]上的最大值()M a .

21. 对于函数()y f x =与常数a 、b ，若(2)()f x af x b =+

恒成立，则称(,)a b 为函数()f x 的一个“P 数对”，若(2)()f x af x b ≥+恒成立，则称(,)a b 为函数()f x 的一个“类P 数对”，设函数()f x 的定义域为+R ，且(1)3f =.

2017 2018上海市上海中学高一上学期周练英语试题

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2018-2019学年上海中学高三上英语期中英语试卷

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上海高中高考数学知识点总结(大全)

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