Question

What are the amplitude, period, phase shift, and midline of f(x) = −3 sin(4x − π) + 2? (6 points)

Amplitude: 3; period: pi over 2 ; phase shift: x = pi over 4 ; midline: y = 2
Amplitude: −3; period: pi over 2 ; phase shift: x = pi over 2 ; midline: y = 2
Amplitude: 2; period: pi over 4 ; phase shift: x = pi over 4 ; midline: y = −3
Amplitude: 2; period: pi over 4 ; phase shift: x = pi over 2 ; midline: y = −3

Answer 1

Amplitude: 3

period: π/2

Phase shift: π/4

Midline : y=2

Explanation:

We are asked to find the amplitude, period, phase shift and midline of the given function f(x) as:

f(x)= -3 sin (4x-π)+2

f(x)= -3 sin (-(π-4x))+2

f(x)= -3 -( sin (π-4x))+2 ( since sin(-θ)=-sin (θ) )

f(x)=3 sin 4x+2 ( since sin (π-θ)=sin (θ) )

• Now The Amplitude is the height from the center line to the peak.

Hence, the amplitude is 3 units.

• we know that period of sin (x) is 2π.

Hence, period of 4x is:

2π/4=π/2.

• The Phase Shift is how far the function is shifted horizontally from the usual position.

Hence, the phase shift is: π/4

• Also midline is the line which divide the graph in equal units in above and below.'

Hence, here we have midline y=2.

Answer 2

The parent function of
`y=-3sin(4x- \pi )+2` is
`y=sin(x)`

The diagrams below show step by step transformation

As we can see from the graph
`y=-3sin(4x- \pi )+2`, the amplitude of the function is 3, period of
`( \pi )/(2)`, phase shift of π and midline y=2