Determining if a Relation is a Function

For a function, each $x$-value cannot give more than one $y$-value. For this graph, however, almost all of the $x$-values give two $y$-values. For example, consider $x=4.$ For that $x$-value, $y$ can be both $\text{-}2$ and $2.$

Thus, the graph fails the vertical line test, and is not a function.