Question

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

Answer 1

Amplitude: 3; period: pi/2; midline: y = 2

Answer 2

Answer:

The amplitude of the function is 3, period of the function is $\frac{\pi}{2}$ and midline of the function is 2.

Step-by-step 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 $\frac{2\pi}{b}$ 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

$\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}$

The midline of the function is

$d=2$

Therefore the amplitude of the function is 3, period of the function is $\frac{\pi}{2}$ and midline of the function is 2.