Question

only plot the first stated period when plotting. From where it's shifted start begins to the end of that period and nothing else.

Answer 1

`\begin{gathered} y=A\sin(B(x+C))+D \\ Period:(2\pi)/(B) \end{gathered}`

For the given function:

`\begin{gathered} y=2\sin(x+(\pi)/(4))+2 \\ \\ B=1 \\ \\ Period:(2\pi)/(1)=2\pi \end{gathered}`

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: