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Match the function with its graph and justify your reasoning.

(a) f (x, y) = sin x  -  sin y 

(b) f (x, y) = sin(x -  y)

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We can distinguish the two functions by looking at the sections y = k for k  R a constant. 

(a) For the function f (x, y) = sin x - sin y these sections are z = sin x - sin k. In other words the graph z = sin x is shifted up and down as y varies. 

(b) For the function f (x, y) = sin(x - y) these sections are z = sin(x- k). In other words the graph z = sin x is shifted to the right and to the left as y varies. 

So we conclude that the right correspondences are (1) – (b) and (2) – (a).

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