Relations, Lines & Functions

(-5, -3), (-2,0), (1,3), (4,6), (7,9)

Domain (all the x-values): {-5, -2, 1, 4, 7}

Range (all the y-values): {-3, 0, 3, 6, 9}

A relation can be any kind of relationship between sets of numbers, FUNCTIONs are a special kind of relationship where EVERY INPUT MUST HAVE EXACTLY ONE OUTPUT.

In other words, the x-value cannot repeat

Vertical Line Test

You can easily determine if a relation is a function by graphing it and doing a vertical line test. Just draw a vertical line (or two) on the graph - if your vertical line ever touches two points of the relation, it's not a function. In other words, the vertical line test proves that none of the x-values repeat, and a relation is a function if none of the domain numbers (x-coordinates) repeat.