Answer
The Amplitude is $ 5$
The Period is $\frac{2\pi}{3}$
The Horizontal shift is $\frac {\pi}{12}$ units to the right
See graph below.
Work Step by Step
For $y=a\sin c(x−h) + k$ $y =a \cos c(x−h) + k$,
Amplitude: $|a|$, Period: $\frac{2\pi} {|c|}$,
Horizontal Shift: h
The question asks for a graph, amplitude, period, and horizontal shift of the function.
Given $y = 5\sin (3x - \frac{\pi}{4})$
$y = 5\sin 3(x - \frac{\pi}{12})$
The Amplitude is $|5| = 5$
The Period is $\frac{2\pi}{|3|} = \frac{2\pi}{3}$
The Horizontal shift is $\frac {\pi}{12}$ units to the right
See graph below.