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

Answer:

So the amplitude is 7

The period is pi

The phase shift is negative pi/2

The midline is -3

Step-by-step 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

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

The phase shift is

$2x + \pi = 0$

$2x = - \pi$

$x = - \frac{\pi}{2}$

So the amplitude is 7

The period is pi

The phase shift is negative pi/2

The midline is -3.