C. Functions are Relations

Functions are a specific type of relation. A function yields one output value for every input value.

Function
for every unique input value, there is a single output value


Note that a relation is not always a function because a relation can have numerous output values for the same input value. A function, by definition, does not.

However, functions do not have to be linear either. Let's explore how to determine whether a relation is a function based on the many ways they can both be represented.

 

Example 1

Determine whether the mapping diagrams below represent functions. Explain.

This mapping diagram represents a function. Each domain value (input value) has exactly one range value (output value).

This mapping diagram does not represent a function. The domain value of 4 has two range values.


 

Example 2

Determine whether the tables of values below represent functions. Explain.

This table of values does not represent a function. The input value of 2 has two output values.

This table of values represents a function. Each input value has exactly one output value.