Question

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

Answer 1

If f(x) is
\[f(x)=A \cos (Bx+C)+D\]
where |A| is the amplitude
The period is
\[T=\frac{2 \pi}{B}\]
The phase shift is
\[\frac{C}{B}\]
and the 'y' shift is D

Answer 2

These are my options:


amplitude = 3; period = pi over two; phase shift: x = negative pi over four

amplitude = −3; period = pi over two; phase shift: x = pi over four

amplitude = −3; period = negative pi over two; phase shift: x = negative pi over four

amplitude = 3; period = 2π; phase shift: x = negative pi over four



Would it be the second one?

Answer 3

In the general equation that I gave above, |A| is the amplitude.
So what does |-3| equal?

Answer 4

-3 = A ?

Answer 5

Not really.
|-x| = x
So |-3| = ?

Answer 6

Oh, -3 = 3 ?

Answer 7

Well, |-3| = 3.
So the amplitude is 3. Therefore the second and third choices can be eliminated.

Answer 8

Oh I see. So, D doesn't look right; it would be A?

Answer 9

Why do you say that D doesn't look right?
Hint: Find the period.