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## What is the amplitude, period, and phase shift of f(x) = −3 cos(4x + π) + 6?

The general form of the cosine function is:

y = A cos(Bx – C) + D

where:

|A| is the amplitude of the function.

The period of the function is: 2π/B

The phase shift of the function is: C/B

A positive phase shift means the graph has moved to the left, while a negative phase shift means the graph has moved to the right.

‘D’ is the amount of vertical displacement, or ‘y’ shift, of the mid point of the function above the ‘x’ axis.

so in this case:

f(x) = −3 cos(4x – π) + 6

A = |-3| = 3

period = 2π/B = 2π/4 = π/2

The phase shift = C/B = -π/4

A) => answer

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