Question

If the relationships below are given in the form (input, output), which pairing always describes a function?
(a person’s age in years, that same person’s height in inches)
(a person’s weight in pounds, that same person’s height in inches)
(a person’s height in centimeters, that same person’s height in inches)
(a person’s telephone number, that same person’s height in inches)

Answer 1

Only the third pairing always describes a function:

- (a person’s height in centimeters, that same person’s height in inches)

Reason: given a height in cm there is exactly one corresponding height in inches (inches = cm ÷ 2.54).

Counterexamples for the others:
- (age → height): two different people can have the same age but different heights.
- (weight → height): two people can have the same weight but different heights.
- (telephone number → height): a phone number can be shared (e.g., household), so one number can correspond to different people with different heights.