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Determine the range of each function: (i) f: R -> R defined by f(x) = 3x + 5; (ii) f: [-1, 5] -> R defined by f(x) = 3x + 5.

1. (i) R, (ii) [2, 20]
2. (i) R, (ii) [-1, 5]
3. (i) [5, infinity), (ii) [2, 20]
4. (i) R, (ii) [2, 5]

Correct answer: (i) R, (ii) [2, 20]

Solution

f(x) = 3x + 5 is increasing. Over all real x its outputs cover all reals, so the range is R. On [-1, 5] the minimum is at x = -1 and the maximum at x = 5, giving a closed interval.

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