Question

What are the amplitude, period, phase shift, and midline of f(x) = −4 cos(3x − π) + 1? amplitude: −4; period: pi over 3; phase shift: x = pi over 4; midline: y = −1 amplitude: 4; period: pi over 3; phase shift: x = pi over 4; midline: y = 1 amplitude: −4; period: 2 pi over 3; phase shift: x = pi over 3; midline: y = −1 amplitude: 4; period: 2 pi over 3; phase shift: x = pi over 3; midline: y = 1?

Answer 1

Alright, lets get started.

The standard form for cos function is

$f(x) = A cos (Bx + C ) + D$

Where

A = Amplitude (positive value)

Period = $\frac{2\pi}{B}$

Phase shift = $\frac{-C}{B}$

Mid line or vertical shift = D

So, comparing the given function with standard

$f(x) = - 4 cos (3x- \pi ) + 1$

A = 4

B = 3

C= $- \pi$

D = 1

Means Amplitude = 4

Period = $\frac{2\pi}{B} = \frac{2\pi}{3}$

Phase shift = $- \frac{C}{B} = \frac{\pi}{3}$

Mid line = 1

Hence the answer is last choice 4.

Hope it will help :)