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 =
`(2\pi)/(B)`

Phase shift =
`(-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 =
`(2\pi)/(B) = (2\pi)/(3)`

Phase shift =
`- (C)/(B) = (\pi)/(3)`

Mid line = 1

Hence the answer is last choice 4.

Hope it will help :)