Question

The table shows the low temperatures in degrees Fahrenheit for the past week in Sioux Falls, Idaho. Define the domain and range of the function and state whether it is one-to-one, onto, both, or neither.



Day 1 2 3 4 5 6 7
Low Temp. 56 52 44 41 43 46 53

Answer 1

Domain: {1, 2, 3, 4, 5, 6, 7} (the days).
Range: {56, 52, 44, 41, 43, 46, 53} (the low temperatures).

Each day maps to a different temperature (no repeats), so the function is one-to-one (injective).
Whether it is onto (surjective) depends on the chosen codomain: it is onto if the codomain is taken to be the set {56,52,44,41,43,46,53}, but not onto if the codomain is a larger set (e.g. all real numbers or all possible temperatures).