问题 填空题
定义在R上的函数f(x)满足f(x+
3
2
)+f(x)=0
,且函数y=f(x-
3
4
)
为奇函数,给出下列命题:
(1)函数f(x)的周期为
3
2

(2)函数f(x)关于点(-
3
4
,0)
对称,
(3)函数f(x)关于y轴对称.其中正确的是______.
答案

由题意定义在R上的函数y=f(x)满足条件 f(x+

3
2
)=-f(x),

故有 f(x+

3
2
)=-f(x)=f(x-
3
2
)恒成立,故函数周期是3,

故(1)错;

又函数 y=f(x-

3
4
)是奇函数,其图象关于原点对称,

而函数y=f(x)的图象可由函数 y=f(x-

3
4
)的图象向左平移
3
4
个单位得到,

故函数y=f(x)的图象关于点 (-

3
4
,0)对称,

由此知(2)(3)是正确的选项,

故答案为:(2)(3)

问答题 简答题
阅读理解

阅读理解。

     It was early afternoon and the harbor (海港) was quiet. Mr Bates, the keeper of the lighthouse (灯塔), went

to the village. He left his daughters Rebecca and Abigail to look after the lighthouse.

     As Rebecca was about to prepare some water for the evening meal, she noticed a strange ship coming to

the harbor. It stopped and lowered two little boats, which turned and started toward land: At that time people

feared every ship they did not know, for the year was 1814 and America and Britain were at war.

     Rebecca and Abigail held their breath to see what these two boats would do. Closer and closer they came,

until finally they entered the harbor. They were full of British soldiers!

     No help was to be seen. What could they do? How could they warn the town soldiers? They had no boat,

and there would be no time to run to the village. Rebecca thought fast and then she had an idea. Calling to

Abigail to follow, she ran to the room where the guns were stored. But instead of reaching for the guns, she

took hold of the fife (军笛 ) and the drum(战鼓 ).

     Then the two young women ran along the wooded path to the shore (海岸). Hiding behind tall trees, they

started to play the fife and the drum. Abigail beat out Roll Call. Rebecca joined in with Yankee Doodle. Soon

 Rebecca saw the boats had stopped!

The girls went on playing. A moment later, a flag was raised on the warship-the signal for the boats to return.

Once everyone was on board, the enemy ship set sail for the open sea.

     The British were fooled, and the" American Army of Two" won the day.

1. Why did Rebecca take the fife and the drum instead of the guns?

A. She would leave the guns for the soldiers.

B. She would welcome the British soldiers.

C. She loved to play the fife and the drum.

D. She wanted to frighten the British soldiers away.

2. The underlined part " American Army of Two" in the last paragraph probably refers to____.

A. Rebecca and Abigail

B. the two British boats

C. the fife and the drum

D. the two town soldiers

3. The British ship left the harbor because____.

A. the British found the weather was too bad

B. a lot of American ships came to stop the British

C. the British thought the American soldiers were coming

D. some of the British soldiers were killed by the American

4. Which of the following words could NOT be used to describe Rebecca and Abigail's action?____

A. Brave.

B. Honest.

C. Clever.

D. Great.