We are asked how to use different representations of relations to determine whether they are functions. Let's begin by recalling the definition of function.

Function
A relation is a function when each input is assigned exactly one output.

Let's take a look at the different ways that we can use to represent relations. These include mapping diagrams, sets of ordered pairs, and tables, to name a few.

Let's analyze each method, one at a time!

Mapping Diagram

If the relation is given as a mapping diagram, we focus in the arrows drawn from the inputs. If there is more than one arrow coming out of an input, the relation is not a function.

Set of Ordered Pairs

In an ordered pair, the $first$ coordinate corresponds to the $input$ and the $second$ to the $output .$

To determine if the relation is a function, we focus on the inputs. The relation is not a function if there is a repeated input.

Three different sets of ordened pairs where one represents a function

Table

A table can be considered in a way similar to the set of coordinate pairs.

Please note that there are more ways of representing relations. We explored only three of these representations here.

Exercise