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

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.