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《1.2 函数及其表示》一课一练2

1.2 函数及其表示

一、选择题

1、设集合A ={x |0≤x ≤6},B ={y |0≤y ≤2},从A 到B 的对应法则f 不是映射的是( )

A 、f :x →y =21x

B 、f :x →y =31x

C 、f :x →y =

4

1x

D 、f :x →y =

6

1x

2、设M ={x |-2≤x ≤2},N ={y |0≤y ≤2},函数f (x )的定义域为M ,值域为N ,则f (x )的图象可以是( )

3、在映射中B A f →:,},|),{(R y x y x B A ∈==,且),(),(:y x y x y x f +-→,则与A 中的元素)2,1(-对应的B 中的元素为( )

A 、)1,3(-

B 、)3,1(

C 、)3,1(--

D 、)1,3(

4、下列各组函数)()(x g x f 与的图象相同的是( )

A 、2

)()(,)(x x g x x f ==

B 、2

2)1()(,)(+==x x g x x f

C 、0

)(,1)(x x g x f ==

D 、?

?

?-==x x

x g x x f )(|,|)( )0()0(<≥x x 5、若{}2

1,,

0,,b a a a b a ?

?=+???

?

,则20052005a

b +的值为( ) A 、0 B 、1 C 、1- D 、1或1-

6、如下图可作为函数)(x f =的图像的是( )

B

C

D

7、若:f A B →能构成映射,下列说法正确的有 ( )

(1)A 中的任一元素在B 中必须有像且唯一;(2)B 中的多个元素可以在A 中有相同的原像;(3)B 中的元素可以在A 中无原像;(4)像的集合就是集合B 。

A 、1个

B 、2个

C 、3个

D 、4个 二、填空题

8、设函数f (x )=???≤,

<,+)2(2)2(22x x x x 则f (-4)=____,又知f (0x )=8,则0x =____

9、如图,有一块边长为a 的正方形铁皮,将其四个角各截去一个边长为x 的小正方形,然后折成一个无盖的盒子,写出体积V 以x 为自变量的函数式是_____,这个函数的定义域为_______

10、给定映射f :(x ,y )→(x ,x +y ),在映射f 下象(2,3)的原象是(a ,b ),则函数f (x )=ax 2+bx 的顶点坐标是________

11、设2

2 (1)

() (12)2 (2)x x f x x x x x +-??=-<

≤≥,若()3f x =,则x=____________。

12、已知2

2

1)1(x

x x

x f +

=-,则=+

)1(x

x f ___________。

三、解答题

13、设f(x)是R 上的函数,且满足f(0)=1,并且对任意实数x 、y ,有f(x-y)=f(x)-y(2x-y+1),求f(x)的表达式。

14、已知二次函数f(x)当x=2时有最大值16,它的图像截x 轴所得的线段长为8,求解析式y=f(x)。

15、已知二次函数f (x )=ax 2+bx (a ,b 为常数,且a ≠0)满足条件: f (x -1)=f (3-x )且方程f (x )=2x 有等根. (1)求f (x )的解析式;

(2)是否存在实数m ,n (m

参考答案

一、选择题1、A ; 2、B ;3、A ;4、D ;5、C ;6、D ;7、C 二、填空题

8、 18 , 4或-6; 9、 V =2)2(x a x -{x |0<x <a /2} 10、(

8

1,-

16

1) 11

12、412

2++

x

x

三、解答题

13、解:因为对于R y x ∈,有f(x-y)=f(x)-y(2x-y+1),令x=0得f(-y)=f(0)-y(-y+1) 所以1)(2+-=-y y y f ,所以)(1)(2R y y y y f ∈++=。 所以)(1)(2R x x x x f ∈++=。

14、解:由题意设16)2()(2+-=x a x f ,即a ax ax x f 4164)(2++-=。 方程041642=++-a ax ax 的两根,21,x x 满足8||21=-x x , 而a

x x x x x x 644)(||212

212

21-=-+=-,所以2

864=-

a

,所以a=-1

所以,124)(2++-=x x x f

15、解:(1)∵方程ax 2

+bx -2x=0有等根,∴△=(b -2)2

=0,得b=2。 由f(x -1)=f(3-x)知此函数图像的对称轴方程为x=-a

b 2=1,得a=-1,

故f(x)=-x 2+2x.

(2)∵f(x)=-(x -1)2+1≤1,∴4n≤1,即n≤

4

1.

而抛物线y=-x 2+2x 的对称轴为x=1,∴当n≤

4

1时,f(x)在[m,n]上为增函数。

若满足题设条件的m,n 存在,则?

??==n n f m m f 4)(4)(

即?????=+-=+-n

n n m

m m 42422

2

????-==-==2020n n m m 或或又m

∴m=-2,n=0,这时,定义域为[-2,0],值域为[-8,0]. 由以上知满足条件的m,n 存在,m=-2,n=0.

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二、Yes?——Pardon——Yes,it is. 三、1手提包2雨伞3课桌4桌子5衬衫6原谅7手表8外套9连衣裙10裙子 四、1.Is this your umbrella? 2.Is that your watch? 3.Is this his shirt? 4.Are they your classmates? Lesson3-4 二.Here is my ticket.—Here is your umbrella and your coat.—Sorry,sir.—No,it isn’t.—Yes,it is. 三.1.小汽车2.房子3.套装4.学校5.教师6儿子7.女儿8.票9.号码10.公交车 四.1.This isn’t my watch. 2.That isn’t your suit. 3.This isn’t their school. Lesson5-6 二、Good morning.—This is Alice.—this is—How do you do? 三、DCBDDD 四、1.早上2.下午3.晚上4.学生5.瑞典的6.法国人7.德国人8.美国人9.英国人10.俄罗斯人 五、1.What’s your name?2.What make is it? 3.What colour is it? 4.What nationality is he? 5.What row are you in? Lesson7-8 二、What nationality are you?—I’m not.—What’s your job?—What’s your job? 三、ADCBCDC 四、1.I am a new student. 2.What nationality are you? 3..Mr. Blake is your teacher. 4.My coat and my umbrella,please. 5.Here is my ticket. 6.Alice is a new student. She is French. 7.What is your job? 五、1.Is she their daughter? 2.He isn’t our teacher. 3.Whose car is it? 4.is 5.Is he a policeman? he is. 6.his Lesson9-10 二、1.an 2.an 3.an 4.an the 5.The 6.a 三、1 its 2 thin 3 long\tall 4 dirty 5 hot 6 old 7 lazy 8 father 9 sister 10 his 四、1.I’m very well. 2.Nice to meet you,too. 3.Good morning. 4.She’s fine,thanks. Lesson11-12 二、1.His 2.your 3.you 4.my 5.Her 6.his 7.It 8.her 9.Steven’s 10.Hers 三、1.Whose car is it? 2.Is this your shirt? 3.He isn’t a policeman. 4.Whose boluse is that? Lesson13-14 二.1colour 2.可爱的3.连衣裙 4.到楼上5.green 6.看7.帽子8.领带9.衬衣10.地毯 11.dog 12 连衣裙 三.1.BDCEAF 2.CADBFEC 四、1-C 2-E 3-A 4-B 5-F 6-H 7-D 8-G

新概念第一册一课一练Lesson

L e s s o n19T i r e d a n d t h i r s t y 一、听力 Mother: _________’s the matter, children? Girl: We’re tired… Boy: …and _______,Mum. Mother: Sit down ________. Boy Girl 三. 1.__________the matter with you? A.What B.How C.What’s 2.The door isn’t shut.It is ___________. A .open B.tall C.heavy 3.Look________the fat man. A.in B.at C. into 4.I want __________ice cream. A.a B.an C.the

5.__________apples are very nice. A.That B.This C.These 6.---Are you ________now?—Yes,I am.Thank you A.all right B.right C./ 7. There are two birds in the tree. I can’t them . A. look B. look at C. watch D. find 8. There 5 apples , but I bananas.

4. Can you play ( the, a, / ) tennis with me ? 七、阅读短文。 根据短文内容,回答下列问题。 Mr. Brown lives near Mr. Smith’s house and they are good friends. Mr. Smith and some other people often call him. “Mr. Going To Do”. Do you know why? Mr. Brown always says he is going to do something, but he never does it. Every Saturday Mr. Brown goes to talk with Mr. Smith. “(1) I’m going to wash my car tomorrow.”Mr. Smith usually says, “Are you, Mr. Brown?” He knows his friend is not going to clean his car. Then he says, “Well, excuse me. I’m going to do some work in my home.” And so he does. Mr. and Mrs. Smith ” 1. Smith’s 3. 4. 2. two, class_____________________________________________________________________ 3. his, are, these, pictures_____________________________________________________________________ 4. color, dress, is, Kate’s, what_____________________________________________________________________ 5. that, is, who, old, woman_____________________________________________________________________ 九、作文。

新概念英语第二册课后练习答案lesson29

Lesson 29 练习答案Key to written exercises 1.关键句型练习答案 A What happened:flew(1.6);landed(1.8);landed(1.9);wanted(1.10);did not take(1.11) What has happened:has bought(1.1);has begun(1.1);has flown(11.7-8);has just refused(11.9-10) 2.难点练习答案 1 bring 2 fetch 3 refused 4 deny 5 Very 3.多项选择题答案 1. b 根据课文第3-4行The most surprising thing about it, however, is that it can land anywhere…可以判断只有b.是正确的,it doesn’t need a runway to land on(它着陆时不需要跑道)是课文所暗示的这个飞机的令人惊奇之处。其他3个选择都不能表明这飞机的令人惊奇之处。 2. c 根据课文第7-8行…Captain Fawcett h as flown passengers to many unusual places 和最后一行。。。but Captain Fawcett did not take him because the trip was too dangerous 可以看出c. will fly passengers anywhere except very dangerous places(将载运旅客去任何地方,除了非常危险的地方)是正确的结论,其他3个选择都过于片面和绝对了。 3. c a. who is 句中修饰的词是物而不是人,因此不能用who 做关系代词; b. whom is : whom做定语从句中的宾语,而本句需要的是做主语的关系代词; d. whose is 不合语法 只有c. which is 是正确的,which 既可以做定语从句的主语,又可做宾语。 4. b 这是一个带形容词比较级的句子,已经有连词than. a. most surprising 和 d. most surprised 都是最高级,不合乎语法;d. more surprised 虽然是比较级,但surprised(感到惊奇)主语应该是人,而本句的主语是it,故不能选d; 只有b. more surprising(更令人惊奇的)最合乎语法和题目意思。 5. d

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