Domain and range

Question

Suppose the function g(x) has domain [−3, 7] and range [−5, 2]. Determine the domain and range for g(x − 8) + 1

Answer 1

g(x-8) shifts the graph to the right by 8, increasing x by 8

g(x-8)+1 shifts the graph up by 1, increasing y by 1

{-3+8, 7+8] = [5, 15] = the domain for g(x-8)+1

[-5+1, 2+1] = [-4, 3] = the range for g(x-8)+1

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