In Mathematics, and real life, we use and investigate relations. A relation is a relationship between sets of values. In math, the relation is in equations, between the x-values and y-values of ordered pairs. The set of all x-values is called the domain, and the set of all y-values is called the range. In real life, some examples of the relationships between two quantities could be how the value of a computer is related to its age, how the amount of time it takes for “x” to walk to school is related to the distance to their school, how much a Slurpee costs depends on how much they get, etc.

When representing a relation, we often regard the values of the independent variable (x) as the input, and the values of the dependant variable (y) as the output. There are seven ways to represent the relationship between two quantities (words, table of values, ordered pairs, mapping diagram, equation, graph, function notation) This is what some of those look like…

But before considering how to represent a relation we need to find out the input and output values. (Obviously it would be unnecessary to collect data for every input value. You only choose some of the possible input values, even if the output value could be determined from any input greater than 0, and up to the maximum independent variable (whether it be max speed, max distance, max weight, etc. )). After writing out possible inputs and their outputs, you choose the appropriate representer-and/or fill in the already chosen one with your inputs and outputs.