Question

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

Answer 1

Amplitude =2 ,

Time period =
`(2\pi )/(1)`.

Phase shift = π.

Explanation:

Given : f(x) = 2 sin(x + π) − 4.

To find : What are the amplitude, period, phase shift, and midline.

Solution : We have given that f(x) = 2 sin(x + π) − 4.

Standard form of sine function : y=Asin(Bx+C) + D.

Where, A = amplitude , Time period =
`(2\pi )/(B)`, C = phaseshift

Midline , D = vertical shift.

On comparing

amplitude =2 ,

Time period =
`(2\pi )/(x)`.

Phase shift = π.

Therefore, amplitude =2 ,

Time period =
`(2\pi )/(1)`.

Phase shift = π.

Answer 2

given that f(x)=2sin(x+π), the standard form of sine function is y=A=sin(Bx+C), with:
A=amplitude
2π/B=period
C/B=phase-shift
A=2=amplitude
B=1
period=2π/B=2π/1=2π
C=2π/1=2π