What are the amplitude, period, and midline of f(x) = 3 cos(4x − π) + 2?

Question

asked Dec 18, 2018 172k views

2 Answers

Boindiil · Answer 1 · 2018-12-23T18:28:32+0000

Answer:

The amplitude of the function is 3, period of the function is
$(\pi)/(2)$ and midline of the function is 2.

Explanation:

The given function is

$f(x)=3\cos(4x-\pi)+2$ .... (1)

The standard form of a Cosine function is

$g(x)=a\cos(bx+c)+d$ ... (2)

where, a is amplitude, period is
$(2\pi)/(b)$ and d is midline.

From (1) and (2), we get

a=3,b=4,d=2

The amplitude of the function is

a=3

The period of the function is

$(2\pi)/(b)=(2\pi)/(4)=(\pi)/(2)$

The midline of the function is

d=2

Therefore the amplitude of the function is 3, period of the function is
$(\pi)/(2)$ and midline of the function is 2.