Question

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

Answer 1

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 $\frac{ \pi }{2}$, phase shift of π and midline y=2

Answer 2

Answer:

Amplitude: 3

period: π/2

Phase shift: π/4

Midline : y=2

Step-by-step 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.