How do you find the amplitude, period, and shift for f(x)=−4cos(3x−π)+1?

(a) Amplitude = 4

(b) --- Period

(c)

--- phase shift

--- vertical shift

Step-by-step explanation:

Given

Rewrite the function as:

Solving (a): The amplitude

A cosine function is represented as:

Where:

So, in this equation (by comparison):

The amplitude is 4

Solving (b): The period (T)

This is calculated as:

By comparison:

So:

Solving (c): The shift

The phase shift is C

The vertical shift is D

By comparison:

--- phase shift

--- vertical shift

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step-by-step explanation:

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