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A function y = f(x) has domain [4, 7] and range [-1, 9]. For each transformed function, state its domain and range: (i) g(x) = (1/3) f(x); (ii) h(x) = f(x - 7).

1. g: domain [4,7], range [-1/3, 3]; h: domain [11,14], range [-1, 9]
2. g: domain [4,7], range [-1, 9]; h: domain [4,7], range [-1, 9]
3. g: domain [12,21], range [-1, 9]; h: domain [-3, 0], range [-1, 9]
4. g: domain [4,7], range [-3, 27]; h: domain [11,14], range [-8, 2]

Correct answer: g: domain [4,7], range [-1/3, 3]; h: domain [11,14], range [-1, 9]

Solution

(i) g(x) = (1/3)f(x) uses the same input x, so domain stays [4,7]; outputs are scaled by 1/3, so range becomes [-1/3, 3]. (ii) h(x) = f(x-7) requires the argument x-7 to lie in [4,7], i.e. x in [11,14]; the output values are unchanged, so range stays [-1, 9].

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