问题 解答题

对于函数f(x),若存在x0∈R,使得f(x0)=x0成立,则称x0为f(x)的不动点.已知函数f(x)=ax2+(b-7)x+18的两个不动点分别是-3和2:

(Ⅰ)求a,b的值及f(x)的表达式;

(Ⅱ)当函数f(x)的定义域是[0,1]时,求函数f(x)的值域.

答案

(Ⅰ)依题意得f(-3)=-3,f(2)=2;

即9a+21-3b-a-ab=-3,4a+2b-14-a-ab=2,解得a=-3,b=5a,b=-15

∴f(x)=-3x2-2x+18

(Ⅱ)∵函数f(x)的对称轴x=-

1
3
,且图象开口向下,

所以函数f(x)在区间[0,1]上单调递减,∴f(x)max=f(0)=18,f(x)min=f(1)=13

所以函数f(x)的值域为[13,18]

阅读理解

Some diaries from Jackie Chan’s blog

January 4, 2009

Lately I’ve been busy in Beijing having meetings to discuss my new movie. I also attended John Wu’s ceremony(典礼)of his new movie, Red Cliff, which took two years to complete. I’m good friends with the director John Wu and the main actor Tony Leung.

January 5, 2009

Today I went to record a television program for Beijing TV called Volunteers Across China. This TV program is a large-scale reality show that is based on the idea that “good people reap good rewards” and it hopes to encourage people to be more aware and help the “good people” who are in difficult situations.

January 6, 2009

I’m very pleased to announce that my Jackie Chan automobile website is set up and officially operating! I hope that through this automotive website, I can get in touch with more people who want to buy cars.

January 7, 2009

Today, I went to record a song called Zhongguo Nian. This song was written by Chang Shilei. I sing this song together with Tan Jing. Chang Shilei is a naturally talented musician. He also has an interesting habit. His piano is placed next to his bed. When he wakes up, he plays the piano until he’s tired, and then he lies down on his bed to sleep.

January 9, 2009

Today I met with the producer and director of Longwei Xiaozi ,and I also brought along my friend’s daughter for a screen test. Although my friend’s daughter grew up in China, her English is very good and it just happened by chance that this movie needs a young actress for a part, so I took her along to audition(试演).

小题1:What might be the best title for this passage?

A.My new movie.

B.My busy life.

C.My good friend.

D.My favorite song.小题2: The TV program Volunteers Across China tries to

A.find some rich people who are able to help the poor.

B.encourage people to look after the young.

C.ask people to help “good people” who are in trouble.

D.make China more and more famous all over the word.小题3:The underlined word “announce” in the third paragraph means

A.tell sb sth officially

B.tell sb what you think

C.tell sb to do sth

D.say that sth must happen小题4:With whom does the author sing the song Zhongguo Nian ?

A.John Wu.

B.Tony Leung.

C.Chang Shilei.

D.Tan Jing.小题5:What can we infer from the text?

A.It took the author two years to finish the movie Red Cliff.

B.People who are in trouble can ask Beijing TV for help.

C.Chang Shilei is a famous actor who is good at playing the piano.

D.Longwei Xiaozi needs a young actress for a part who can speak English well.

单项选择题