The relation isn't a function because a function is a relation where each x-value has only one corresponding y-value. Try to put a vertical line through that shape made by the graph to test if it's a function. If it passes through multiple points, it's not a function. For example, if you put the vertical line x=3 in that same graph, it will intersect with the relation at points (3, -3) and (3, 4), and therefore is not a function.
