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].

D: [-1, 3]

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