There are multiple ways to represent function notation. We can relate the domain and range of a function with a table of values, mapping diagram, ordered pairs, a graph, or even function notation. In order to understand how to translate between the various representations of the functions, a verbal description is very useful. Because each representation of a function (words, equation, table or graph) describes the same relationship, you can use one representation to create the others.

For example, if a manager of an amusement park monitors the ticket sales at the park over a four-day weekend, the situation has several variables in order for him to be able to understand how the domain and range are related. He will be able to generate a table of values with the data listing the day of the weekend and the amount of sales taken in that day. He can sketch a graph from this table of values and be able to visually show how the ticket sales depended on what day he was checking.