Domain and Range

Question

Draw a graph with a domain of {x|-6<x<3} and a range of {y|-4≤y≤5}.

Answer 1

y = 1/2 + 9/2 sin x for -3 < x < 6

This has value 5 at x = - 3π/2 and π/2 and value -4 at x = -π/2 Thus, y realizes its maximum range (as sin ranges from -1 to 1), -4 <= y <= 5, and x has the desired domain.