A series of points in the form (x, y) is a function if every -value is different.
A graph is a function of a vertical line passes through the graph at most time.
In other words, a series of points is a function if each input (x-value) corresponds to exactly one output (y-value), and no two different inputs correspond to the same output.
On a graph, if a vertical line intersects the graph at more than one point, then the graph is not a function. This is because for a given x-value, there would be more than one corresponding y-value, violating the definition of a function.