A typical graph of y=sinx has domain for all values of x and range is from [−1,1].
It is a cyclical curve and repeats after every 2π, hence its period is 2π.
It's value is 0 at each nπ, it touches a maximum value of 1 at each 2nπ+π2 and a minimum value of −1 at each 2nπ−π2 (where n is an integer).
It appears like graph{sin(x) [-10, 10, -2, 2]}
If we draw the graph of y=2sin(x+π), the range will be doubled due to multiplier 2 and will be [−2,2].
However, the graph will be shifted by π and hence minimum value will be −2 at each 2nπ+π2 and a maximum value of −2 at each 2nπ−π2 (where n is an integer). But the function will continue to have value 0 at each nπ.
As the period of curve is 2π, it does not matter whether you say it has shifted by π to the left or right.
The graph of 2sin(x+π) appears like graph{2sin(x+pi) [-10, 10, -2, 2]}
