This relation is not a function. Each input (domain or x value) must have only one output (range or y value). If you look at some of the x values, there are two points where the relation will intersect the x value.
For example, on this question (points aren't exact, this is just from perspective) there are points (1,1) and (1,-1). As you can see, this one has two outputs, so it is not a function.
A good way to test to see if a relation is a function is the "vertical line test". You draw (or imagine just to be a quick) a vertical line down towards the graphed relation. This vertical line can only intersect with the graphed relation ONCE. If it intersects with two parts of the relation, it is not a function.
In this scenario, if you drew a vertical line down at x=5, it would intersect with the relation at about 2 and negative 2. Since it intersected twice with the graphed relation, it is not a function.
