问题 填空题

符号[x]表示不超过x的最大整数,如[2.3]=2,[-1.3]=-2.若定义函数f(x)=x+[x],则下列命题中所有不正确命题的序号为______.

①函数f(x)的定义域为R;  

②函数f(x)的值域为R;   

③函数f(x)是奇函数;

④函数f(x)是周期函数;    

⑤函数f(x)是R上的增函数.

答案

①由题意可得,函数f(x)的定义域为R; 故①正确 

②由X的取值任意可得,x+[x]取值任意,即函数f(x)的值域为R,故②正确

③∵函数f(x)=x+[x],则f(-x)=-x+[-x]

例如f(3.5)=3.5+[3.5]=3.5+3=6.5,而f(-3.5)=-3.5+[-3.5]=-3.5-4=-7.5≠-f(3.5)

则函数不是奇函数;故③错误

④由函数f(x)=x+[x]可得,由函数为单调递增函数可知,函数不是周期函数,故④错误

⑤显然,随着x的增加,x+[x]逐渐增加,即函数f(x)是R上的增函数.故⑤正确

故答案为:③④

阅读理解

People express their personalities in their clothes, their cars, and their homes. Our diets can also show our personalities because we might choose certain food to tell people something about us.

For example, some people mainly enjoy high quality food, such as caviar (鱼子酱) and lobster (龙虾), and they eat only in expensive restaurants – never in cafeterias or bars. They know about the “better things in life”.

Some people choose not to eat meat. Vegetarians often have more in common than just their diet. Their personalities might be similar too. For instance, vegetarians in the United States and Canada may be creative people, and they might not enjoy competitive sports or jobs. They worry about the health of the world, and they are probably strongly against the war.

Some people eat mostly fast food. One study shows that many fast-food eaters have a lot in common, but they are very different from vegetarians. They are competitive and good at business. They are also usually in a hurry. Many fast-food eaters might not agree with this description of their personalities, but it is a common picture of them.

Some people also believe that people of the same astrological sign(星座)have similar food personalities. Aries (born under the sign of Aries, between March 21 and April 20) usually like spicy foods, with a lot of onions and pepper. People with the sign of Taurus (April 21 to May 22) prefer healthful fruits and vegetables, but they often eat too much. Sagittarius (November 22 to December.22) like traditional food from many different countries.

What is your food personality?

小题1:Why do some people mainly eat high quality food?

A.They want to show off their wealth.

B.Food can show off their social position.

C.They want to enjoy better things in life.

D.They are wiser than any other persons.小题2:A vegetarian may be a person________.

A.who is believed to be a peace – lover

B.who values the importance of success

C.who cares little about the future of the world

D.who shows his power to make money小题3:From the passage, we can draw a conclusion that_____________.

A.food is just a mirror of the human history

B.we can know a person from what he eats

C.people are particular about the food they eat

D.what people eat may change their personalities

填空题