问题 填空题
某同学利用描点法画函数y=Asin(ωx+∅)(其中A>0,0<ω<2,-
π
2
<ϕ<
π
2
)的图象,列出的部分数据如表:
x01234
y101-1-2
经检查,发现表格中恰有一组数据计算错误,请你根据上述信息推断函数y=Asin(ωx+∅)的解析式应是y=______.
答案

由题意可知(0,1),(2,1)关于对称轴对称,且对称轴x=1,

由三角函数的对称性可知,正弦函数在对称轴处取得最大值,且过(1,A),

从而可得第二組(1,0)错误

把(1,A)代入可得,ω+∅=

π
2

(2,1),(3,-1)关于(

5
2
,0)对称,所以可得(
5
2
,0)
是函数的对称轴x=1相邻一个对称中心

从而函数的周期T=4×(

5
2
-1)=6,根据周期公式T=
ω
=6
,∴ω=
π
3
,∅=
π
6

函数f(x)=Asin(

π
3
x+
π
6
)

把函数图象上的点(0,1)代入函数解析式可得Asin

π
6
=1,∴A=2

故答案为:2sin(

π
3
x+
π
6
)

阅读理解

Mrs. Blake teaches English in a large school in the inner area of a big city on the west of coast. Even since she was a young girl,she has wanted to become a teacher. She has taught eight years now and hasn‘t changed her mind. After she graduated from high school, she went on to college. Four years later, she received her bachelor’s degree (B A) in English and her teaching certificate(证书)。 Then she went to teach in the secondary schools of her state. In the summers, Mrs. Blake takes more classes; she hopes to get a master‘s degree (M A)。 With an MA, she will receive a higher salary and if possible, she hopes to get a doctor’s degree as well. The school day at Mrs. Blake‘s high school, like that in many high schools in the United States, is divided into one hour each. Mrs. Blake must teach five of these periods. During her free period, which for her is from 2 to 3 P.M. , Mrs. Blake must meet with parents, make out examinations, check assignments at all, Mrs. Blake works continuously from the time she arrives at school in the morning till the time she leaves for home late in the afternoon.

1. How long is it since Mrs. Blake graduated from middle school?

A. four years B. eight years C. twelve years d. twenty years

2. According to the article, which is the right order of the degrees a person can receive after going to university?

A. a doctor‘s degree – a bachelor’s degree – a master‘s degree

B. a bachelor’s degree – a master‘s degree – a doctor’s degree

C. a master‘s degree—a bachelor’s degree – a doctor‘s degree

D. a bachelor’s degree – a doctor‘s degree—a master’s degree

3. How many degrees has Mrs. Blake achieved so far?

A. one   B. two    C. three   D. none

4. Which of the following sentences is not true?

A. Mrs. Blake teaches in the inner area of big city on the east of the United Sates

B. Mrs. Blake has turned her wish of becoming a teacher into reality.

C. Mrs. Blake is still studying in her holidays in order to get higher degrees.

D. The working hours in the school where Mrs. Blake works are similar to those of many other high schools in the states.

选择题