Question

What are the following of this function y = 4sin (2( x - $\frac{3\pi }{4}$ )) :
amplitude
minimum
maximum
period
phase shift
midline equation

Answer 1

Answer:

See below...

Step-by-step explanation:

For a function whose formula is in this pattern:

$y=A\sin\left(B(x-C)\right)$

Amplitude: $|A|$

Period: $\frac{2\pi}{B}$

Phase Shift:  C

In this question, $A=4,\,B=2,\,C=\frac{3\pi}{4}$

Amplitude: 4

Period: $\frac{2\pi}{2}=\pi$

Phase Shift: $\frac{3\pi}{4}$

There is no vertical shift, so the midline is the x-axis whose equation is y = 0.

Also, because there is no vertical shift, the maximum is 4 and the minimum is -4.

The graph is attached.