Question

What are the amplitude, period, phase shift, and midline of f(x) = 7 cos(2x + π) − 3? (6 points) Amplitude = −3; period: π; phase shift: x = negative pi over 2 ; midline: y = 3 Amplitude: 7; period: π; phase shift: x = negative pi over 2 ; midline: y = −3 Amplitude: 7; period: 2π; phase shift: x = pi over 2 ; midline: y = 3 Amplitude: −3; period: 2π; phase shift: x = pi over 2 ; midline: y = −3

Answer 1

So the amplitude is 7

The period is pi

The phase shift is negative pi/2

The midline is -3

Explanation:

A trigonometric function is the same as

`f(x) = a \cos(b(x + c)) - d`

Where a is the amplitude, 2 pi/ absolute value of b is the period, c is the phase shift, and d is the vertical shift or midline.

Given the function

`7 \cos(2x + \pi) - 3`

The amplitude is 7, and the midline is -3. The period is

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

The phase shift is

`2x + \pi = 0`

`2x = - \pi`

`x = - (\pi)/(2)`

So the amplitude is 7

The period is pi

The phase shift is negative pi/2

The midline is -3.