Question

What are the amplitude, period, phase shift, and midline of f(x) = −4 cos(3x − π) + 1?

Answer 1

Amplitude: 4; period: 2 pi over 3; phase shift: x = pi over 3; midline: y = 1

Explanation:

Use the form a cos (bx-c)+d to find the amplitude, period, phase shift, and vertical shift.

a=-4

b=3

c=pi

d=1

Answer 2

The general function for the cos function is:

y=Acos(B(x+C)) where A is the amplitude, 2πB is the period and phase shift is C .

For our function: f(x) = −4 cos(3x − π) + 1 =-4cos(3(x-π/3))+1

the amplitude is:-4

the phase shift is: -π/3