问题 选择题

定义在R上的函数满足以下三个条件:

①对任意的x∈R,都有f(x+4)=f(x);

②对任意的x1,x2∈[0,2]且x1<x2,都有f(x1)<f(x2);

③函数f(x+2)的图象关于y轴对称,

则下列结论正确的是(  )

A.f(4.5)<f(7)<f(6.5)

B.f(7)<f(4.5)<f(6.5)

C.f(7)<f(6.5)<f(4.5)

D.f(4.5)<f(6.5)<f(7)

答案

由①可得函数的图象关于直线x=4对称;,由②可得函数在[0,2]上是增函数;

由③可得函数f(x+2)为偶函数,故f(2-x)=f(2+x),故函数f(x)的图象关于直线x=2对称.

综上可得,函数f(x)是周期等于4的周期函数,且函数在[0,2]上是增函数,在[2,4]上是减函数.

再由 f(4.5)=f(0.5),f(7)=f(3)=f(2+1)=f(2-1)=f(1),

f(6.5)=f(2.5)=f(2+0.5)=f(2-0.5)=f(1.5),

故有 f(4.5)<f(7)<f(6.5),

故选A.

阅读理解

阅读理解。

     Many students of English think that learning a new language is very difficult. Now think how difficult it

is to learn English when your brain is only the size of a bird's brain! That is what some birds can do.

     Many different kinds of birds can copy the sounds of language. African grey parrots are the best known

for this.

     Every December in London, the National Cage and Aviary Bird Show tries to find the best "talking" bird

in the world. One bird named Prudle stood out among the "talking birds". She won this prize for 12 years

from 1965 to 1976.

     Prudle was taken from her nest in Uganda in 1958. She was sold to Iris Frost in Seaford, England. Prudle

knew almost 800 words in English.

     Prudle was also the oldest bird in the world that lived in a cage. Ms. Frost took care of the bird until

Prudle died in 1994. Prudle was 35 years old.

     A different kind of bird, not a parrot, named Puck was tested in 1993. It turned out that Puck knew more

English words than Prudle knew. Puck knew more than 1,700 words.

     If a bird can do it, anybody can do it.

1. What kind of birds is the most famous for speaking? [ ]

A. African grey parrots.

B. The birds with big brains.

C. The birds in cages.

D. English parrots.

2. What dose the word "stand out" mean in this passage? [ ]

A. 站出来

B. 飞起来

C. 脱颖而出

D. 取出来

3. How many years did Prudle win the speaking competition for birds? [ ]

A. 35 years.

B. 12 years.

C. 55 years.

D. 8 years.

4. Puck was better than Prudle because ______. [ ]

A. he could fly higher

B. he knew more words

C. he spoke faster

D. he was bigger

5. Who was Iris Frost? [ ]

A. A parrot.

B. Puck's owner.

C. Prudle's owner.

D. An English teacher

单项选择题