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

A person’s height in centimeters, that same person’s height in inches.

Explanation:

For a function to be a well-behaved relation, we must know the point that we are starting from and the next point that we have to move to.

(a person’s age in years, that same person’s height in inches) - these two values telling about a person's age and height are not co-related so it is not a function.

(a person’s weight in pounds, that same person’s height in inches) - these two values telling about a person's weight and height are not co-related so it is not a function.

(a person’s telephone number, that same person’s height in inches) - again a person's phone number does not tell us anything about his height so this is not a function either.

While a person’s height in centimeters can tell us that same person’s height in inches as well so this describes a function.

Answer 2

Answer: A person’s height in centimeters, that same person’s height in inches would be a function.

Explanation:

A relation is said to be a function if it has one single output for each input.

A relation is not said to be a function if any single input has two outputs.

First option is not a function as two person with same age can have two different heights.

Second option is not a function as two person with same weight can have different height .

Third option is a function as If two persons height is same in centimeters then it will same in inches too. Therefore here is only one output for each input.

Fourth option is not a function as it can happen that two persons using same telephone number can have different height.