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.
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.
