Eve’s teacher asked her to graph the function y is equal to negative cotangent times x minus 1 by reflecting the graph of the function y is equal to cotangent of x about the x -axis and translating it vertically. Does it matter in which order Eve does the transformations?

The target function is y = −cot(x) − 1. Reflecting y = cot(x) across the x-axis gives y = −cot(x), and then shifting that graph 1 unit down gives the target. If Eve shifts the original graph down first and then reflects it, the shift also gets reflected, producing y = −cot(x) + 1 instead. So the order matters: reflect first, then translate down, as choice D says.

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