Question

What is the amplitude, period, and phase shift of f(x) = −2 sin(3x − π) − 1?

Amplitude = 2; period = two times pi over three; phase shift: x equals pi over three
Amplitude = −2; period = 2π; phase shift: x equals pi over three
Amplitude = 2; period = two times pi over three; phase shift: x equals negative pi over three
Amplitude = −2; period = 2π; phase shift: x equals negative pi over three

Answer 1

Amplitude = 2; period = two times pi over three; phase shift: x equals pi over three

Explanation:

The given function is
`f(x)=-2 \sin(3x-\pi)-1`

Comparing to
`f(x)=a \sin(bx-c)+d`, we have a=-2 , b=3,
`c=\pi` and d=-1.

The amplitude is
`|a|`.

This implies that amplitude is
`|-2|=2`

The period is
`(2\pi)/(|b|)`

This implies period is
`(2\pi)/(3)`

The phase shift is
`x=(c)/(b)`

This implies that phase shift is
`x=(\pi)/(3)`