问题 填空题
给出定义:若m-
1
2
<x≤m+
1
2
(其中m为整数),则m叫做离实数x最近的整数,记作{x},即{x}=m.在此基础上给出下列关于函数f(x)=|x-{x}|的四个命题:
①函数y=f(x)的定义域是R,值域是[0,
1
2
];
②函数y=f(x)的图象关于直线x=
k
2
(k∈Z)对称;
③函数y=f(x)是周期函数,最小正周期是1;
则其中真命题是______.
答案

①定义域显然为R,然后根据题设x≤m+

1
2
,{x}=m,

则f(x)=x-{x}≤

1
2
,故①成立;

②f(k-x)=|(k-x)-{k-x}|=|(-x)-{-x}|=f(-x),

所以关于x=

k
2
(k∈Z)对称,故②成立;

③f(x+1)=|(x+1)-{x+1}|=|x-{x}|=f(x),

所以周期为1,故③成立.

故答案为:①②③.

填空题
阅读理解

There are numerous similarities between Muhammad Ali and his 23-year-old daughter Laila. She is the only one of his nine sons and daughters to have those genes that led to the ring(拳击场). Her father’s great status had nothing to do with Laila’s decision to pursue a boxing career. She has always been proud of his achievements, but he was never a great man to her—just dad.

What attracted her to take up boxing was the unusual sight of two women in the ring on the television screen when she was about to watch a Mike Tyson fight five years ago. She was very excited and said to herself, “I can do that. ”

Laila’s father would prefer her not to take up the dangerous sport. Johnny McClain, her husband and manager (former boxer himself) feels the same way. Even though both the men in her life worry about her, they’re 100 percent supportive. “They don’t want me to get hurt, ” she says.

Long before entering the ring, Laila was a fighter. Being the daughter of an outstanding boxer made her an easy target for high school kids to see how tough she was. They, not she, failed in the test. For the public, her biggest test took place last summer in the New York State when she took on Jacqui Frazier Lyde, the daughter of Joe Frazier, her father’s most famous opponent (对手) during the 1970s.

That fight provided the biggest shot in the arm that women’s boxing has received. News reporters poured in. Some called it “Ali/Frazier-GenerationⅡ”. No match involving women had ever attracted so much attention. Laila had a narrow victory in the fight.

Like it or not, she accepts the fact that she is the face of female boxing. And she hopes that her name and fame will help get the public to take it more seriously.

The name Ali has and always will bring her attention. But she is determined to make her own mark on opponents’ faces as well as in boxing history books. She says, “I want women’s boxing to get its due respect. ”

小题1:Laila took up boxing because of ________.

A.her father’s great status

B.a Mike Tyson fight

C.her admiration for her father

D.her interest in boxing小题2:From the passage we can know ________.

A.Laila’s husband is still a boxer now

B.Laila wants to make contributions to the sport of boxing

C.Laila’s husband doesn’t think boxing is a dangerous sport

D.when Laila was in high school, she often failed in the fight with other kids小题3:What does the underlined sentence in Para. 5 mean?

A.That fight proved that Laila was a person of physical power.

B.That fight made female boxing more popular.

C.That fight provided people with a good change to enjoy themselves.

D.Laila made her first public appearance in that fight.小题4:Which of the following is the best title for the passsage?

A.A female boxer—Laila Ali

B.The best-known fight

C.Ali/Frazie-GenerationⅡ

D.Muhammad Ali and his daughter