Question

What sine function represents an amplitude of 1, a period of 2π, a horizontal shift of π, and a vertical shift of −4?

Select one:
a. f(x) = sin (x − π) − 4
b. f(x) = sin (πx) + 4
c. f(x) = sin (x + pi over 2 ) + 4
d. f(x) = sin ( pi over 2 x) − 4

Answer 1

Option a. f(x) = sin (x -
`\pi`) - 4 is the required sine function

Explanation:

Step 1 :

Given,

Amplitude = 1

period = 2
`\pi`

horizontal shift =
`\pi`

Vertical shift = -4

Step 2 :

The sine function's equation is as follows :

f(x) = a sin(bx + c) + d

where

a represents the amplitude

b represents the period, obtained by dividing the given period by 2
`\pi`

c represents the horizontal shift

d represents the vertical shift

Step 3:

So here we have,

a = 1

b = 2
`\pi` / 2
`\pi` = 1

c = -
`\pi` (assuming the wave is shifted to the right)

d= -4

Substituting the values in the sine function we get

f(x) = sin (x -
`\pi`) - 4

Step 4:

Answer

option a. f(x) = sin (x -
`\pi`) - 4 is the required sine function