State the amplitude, period, phase shift, and vertical shift of f(x) = −2 sin( (x+1) /4 ) − 3

Answer 1

The "standard form" of a sinusoid, like sine or cosine, gives you all the information you need:

f(x) = Asin[B(x - C)] + D

Where A is the amplitude (ignore any negative signs)

B is used to determine the period. To find the period use Period = 2π/B

C is the phase shift

D is the vertical shift

This function is already in the proper form so the amplitude (A) = 2, Since B = 1/4, then the Period = 2π/(1/4), the Phase Shift (C) = -1 and the vertical shift (D) = -3