问题 选择题

已知函数f(x)的定义域为R.若存在常数c>0,对∀x∈R,有f(x+c)>f(x-c),则称函数f(x) 具有性质P.给定下 * * 个函数:①f(x)=|x|,②f(x)=sinx,③f(x)=x3-x其中,具有性质P的函数的序号是(  )

A.①

B.③

C.①②

D.②③

答案

①因为f(x)=|x|不是R上的增函数,所以不满足f(x+c)>f(x-c),故此函数f(x)不具有具有性质P.

 ②因为f(x)=sinx的最小正周期为2π,不是在R上的增函数,所以不满足f(x+c)>f(x-c),故此函数f(x)不具有性质P.

③∵f(x)=x3-x,∴f′(x)=3x2-1,当f′(x)>0时,函数f(x)是增函数,f′(x)<0时,函数f(x)是递减函数.

即在(-

3
3
3
3
)内递减,要想满足f(x+c)>f(x-c),只须c>
3
3
 就可以了,不妨取c=1,.

所以,存在常数c=1,满足f(x+c)>f(x-c).故此函数f(x)具有性质P.

故选B

单项选择题
阅读理解

阅读理解。

     Somali pirates (海盗) robbed three Thai fishing ships with 77 sailors on board nearly l,200 Miles off the

Somali coast, the farthest-off-shore attack to date, an officer said Tuesday.

     Pirates have gone farther south and east in answer to increased patrols (巡逻) by warships off the Somali

shore. The robbing of the three ships Sunday was about 600 miles outside the normal operation area for the

international force, said a spokesman.

     The spokesman said the attack so far out at sea was a clear sign that the international patrols against pirates

were having a "marked effect on pirate activity in the area".

     "Once they start attacking that far out, you're not even really talking about the Somali basin or areas of water

that have any connection with Somalia," said an officer, Roger Middleton. "Once you're that far out, it's just

the Indian Ocean, and it means you're looking at trade going from the Gulf to Asia, from Asia to South Africa." 

     "This is the farthest robbing to date. They are now operating near the Maldives and India," said another

officer.

     The three ships-the MV Prantalay l l,12, a nd l 4-had 77 members on board in total. All of them are Thai,

the spokesman said. Before the Sunday robbing, pirates held l l ships and 228 sailors.

     Pirates have increased attacks over the past year in hopes of catching more dollar payments. Because of

increased patrols and defenses on board ships, the success rate (率) has gone down, though the number of

successful attacks has stayed the same year over year.

1. The pirate attack reported in the text happened _____.[ ]

A. far out in the Indian Ocean

B. in the normal patrol area

C. near the Somali, coast

D. in the south of Africa

2. According to the text, which can best describe the situation of the pirate problems? [ ]

A. More goods on board are lost.

B. Pirate attacks happen in a larger area now.

C. The number of attacks has stayed the same these years.

D. Pirate attacks are as serious as before along the Somali coast.

3. Which is true about the warship patrols according to the text? [ ]

A. The patrols are of little effect.

B. The patrols are more difficult.

C. More patrols are quite necessary even in Asia.

D. The patrols only drive the pirates to other areas.

4. How many sailors were held by the pirates up to the time of the report? [ ]

A. 228.

B. 77.

C. 383.

D. 305.