Note that the sine function always produces values between -1 and 1.
π in sin(x-π) only shifts the graph of sin(x) horizontally, having no effect on the range, which still is [-1, 1].
Multiplying by 2 (we have 2sin(x-π) ), means that the new range is [-2, 2].
Last, adding 1, means that all the values taken by 2sin(x-π), that is [-2, 2], are now one unit higher in the graphs.
This means that the range is [-2+1, 2+1]=[-1, 3].
Answer: D: [-1, 3]
