Answer
The Amplitude is $3$
The Period is $ 2\pi$
The Horizontal shift is $\frac {\pi}{4}$ units to the left
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 $y = 3 \cos (x + \frac{\pi}{4})$
The Amplitude is $|3| = 3$
The Period is $\frac{2\pi}{|1|} = 2\pi$
The Horizontal shift is $\frac {\pi}{4}$ units to the left
See graph below.
