What is the range of the function y = 1 + 2sin (x - pi) ?

A. - 1 to 1

B. - 2 to 2

C. 0 to 3

D. - 1 to 3

E. - 3 to 3

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]