[tex]\begin{gathered} y=A\sin(B(x+C))+D \\ Period:\frac{2\pi}{B} \end{gathered}[/tex]
For the given function:
[tex]\begin{gathered} y=2\sin(x+\frac{\pi}{4})+2 \\ \\ B=1 \\ \\ Period:\frac{2\pi}{1}=2\pi \end{gathered}[/tex]
Then, the period is 2π; the graph just taking the period is the normal graph of y=sinx (You make the transformations with amplitude (A), and translations (C and D))
Use the graph above you can graph the given function as follow:
A is the amplitude
C is the horizontal translation of the graph
D is the vertical translation
Amplitude:2
Horizontal translation: π/4 to the left
Vertical translation: 2 units up
Graph:
