Question

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

Answer 1

Answer:

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

Step-by-step 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 $\frac{2\pi}{|b|}$

This implies period is $\frac{2\pi}{3}$

The phase shift is $x=\frac{c}{b}$

This implies that phase shift is $x=\frac{\pi}{3}$