Question

The graph is supposed to show f(x)=3sin(x/4+1)-1/2. Which of the following are correctly represented in the graph? Select all that apply. (2 answers)

a. the amplitude
b. the vertical shift
c. the horizontal shift
d. the period
e. the horizontal expansion or compression

Answer 1

a , b, c are only applicable in graph.

Explanation:

Given : The function
`f(x)=3sin((x)/(4)+1)-(1)/(2)`

To find : Which of the following are correctly represented in the graph?

Solution :

General form of sin function is
`y=A sin(B(x-C)+D`

Where A is the amplitude

`B=\frac{2\pi}{\text{Period}}`

D is the vertical shift.

C is the horizontal shift or phase shift.

Comparing with the general form:

`f(x)=3sin((x)/(4)+1)-(1)/(2)`

Transform little bit we get,

`f(x)=3sin((1)/(4)(x-(-4)))-(1)/(2)`

a. Amplitude is
`A=3`

It is correct.

b. Vertical shift is
`D= -(1)/(2)`

it is correct.

c. Horizontal shift
`C=-4`

It is correct.

d. Period is
`P=(2\pi)/(B)`

`P=(2\pi)/((1)/(4))`

`P=8\pi`

It is not correct .

Actual period in graph is
`2\pi`

e. The horizontal expansion or compression

It also not correct because period is not correct.

The expansion and compression depends on the period.

Therefore, a , b, c are only applicable in the graph.

Answer 2

amplitude is correct
The vertical shift is correct
and the horizontal shift is correct