Question

What are the following of this function y = 4sin (2( x -
`(3\pi )/(4)` )) :

amplitude
minimum
maximum
period
phase shift
midline equation

Answer 1

See below...

Explanation:

For a function whose formula is in this pattern:

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

Amplitude:
`|A|`

Period:
`(2\pi)/(B)`

Phase Shift: C

In this question,
`A=4,\,B=2,\,C=(3\pi)/(4)`

Amplitude: 4

Period:
`(2\pi)/(2)=\pi`

Phase Shift:
`(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.