问题 选择题
函数f(x)是定义在R上的偶函数,且对任意的x∈R,都有f(x+2)=f(x).当0≤x≤1时,f(x)=x2.若直线y=x+a与函数y=f(x)的图象有两个不同的公共点,则实数a的值为(  )
A.n(n∈Z)B.2n(n∈Z)
C.2n或2n-
1
4
(n∈Z)
D.n或n-
1
4
(n∈Z)
答案

因为函数f(x)是定义在R上的偶函数,设x∈[-1,0],则-x∈[0,1],于是f(x)=(-x)2=x2

设x∈[1,2],则(x-2)∈[-1,0].于是,f(x)=f(x-2)=(x-2)2

①当a=0时,联立

y=x
y=x2
,解之得
x=0
y=0
x=1
y=1
,即当a=0时,即直线y=x+a与函数y=f(x)的图象有两个不同的公共点.

②当-2<a<0时,只有当直线y=x+a与函数f(x)=x2在区间[0,1)上相切,且与函数f(x)=(x-2)2 在x∈[1,2)上仅有一个交点时才满足条件.由f(x)=2x=1,解得x=

1
2

∴y=(

1
2
)2=
1
4
,故其切点为(
1
2
1
4
)

a=

1
4
-
1
2
=-
1
4

y=x-
1
4
y=(x-2)2
(1≤x<2)解之得
x=
5-2
2
2
y=
9-4
2
4

综上①②可知:直线y=x+a与函数y=f(x)在区间[0,2)上的图象有两个不同的公共点时的a的值为0或-

1
4

又函数f(x)是定义在R上的偶函数,且对任意的x∈R,都有f(x+2)=f(x),实数a的值为2n或2n-

1
4
,(n∈Z).

故应选C.

单项选择题
填空题

Part 4


Questions 26-45


·Read the following passage and choose the best word for each space.
Money spent on advertising is money spent as well as any (26) know of. It serves directly to assist a rapid of goods at reasonable prices, (27) establishing a firm home market and so making it possible to provide (28) export at competitive prices. By drawing attention to new ideas it helps enormously to raise standards of living. By helping to increase demand it (29) an increasing need for labor, and is therefore an effective way to fight unemployment. It lowers the costs of many services: (30) advertisements your daily newspaper would cost four times as much, the price of your television license would need to be doubled, and travel by bus or tube would cost 20 percent more.
And perhaps most important of all, advertising provides a guarantee of reasonable value in the products and services you buy (31) the fact that twenty-seven Acts of Parliament govern the terms of advertising, no regular advertiser dare promote a product that fails to live (32) the promise of his advertisements. He might fool some people for a little (33) through misleading advertising. He will not do so for long, for mercifully the public has the good (34) not to buy the inferior article more than once. If you see an article (35) advertised, it is the surest proof. I know that the article does what is (36) for it, and that it represents good value.
Advertising does more for the (37) benefit of the community than any other force I can think of.
There is one more point I feel I ought to (38) on. Recently I heard a well-known television personality (39) that he was against advertising because it persuades rather than informs. He was drawing (40) fine distinctions. Of course advertising (41) to persuade.
If its message were (42) merely to information—and that in itself (43) difficult if not impossible to achieve, (44) even a detail such as the choice of the color of a shirt is subtly persuasive — advertising would be so boring (45) no one would pay any attention. But perhaps that is what the well-known television personality wants.

A.objective

B.spiritual

C.material

D.subjective