For a relation to be a function, each input value, x, has to corresponds to a single output value, y. So, if a relation has a value of x that outputs more than one value of y, it is not a function. If every x outputs a single value of y, then its a function.
Graphically, a x that outputs more than one y is equivalent toa vertical line that intersecpts the graph more than once.
So, if a graph has at least one vertical line that intercept it more than once, that graph is not a functinon.
In the graph, we can see that in the interval (-2, 2), every vertical line intercepts the graph three times, for example:
So, this graph does not represent a function.
