Question

What are the amplitude, period, and midline of f(x) = 5 sin(x − π) + 3?

A. amplitude: 5; period: π; midline: y = 3

B. amplitude: 3; period: pi/2; midline: y = 5

C. amplitude: 3; period: pi/4; midline: y = 5

D. amplitude: 5; period: 2π; midline: y = 3

Answer 1

Amplitude, A = 5

Mid line, y = 3

Period = 2π

Explanation:

The given equation is
`f(x)=5\sin(x-\pi)+3`

The general sinusoidal equation is

`y=A\sin(Bx+C)+D`

A = Amplitude

D = mid line

C = phase shift

Period = 2π/B

Comparing the given equation, with this general equation, we get

Amplitude, A = 5

Mid line, y = 3

Period = 2π/1= 2π

Looking into the given options, D is the correct option.

Answer 2

amplitude: 5; period: 2π; midline: y = 3