Question

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

Answer 1

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

Step-by-step 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