In these examples, (i) and (iv) represent functions, while (ii) and (iii) do not. In (ii), the graph is a vertical line. Thus, every `y`-value is associated with the same `x`-value. In order to have a function, every `x`-value must be associated with a unique `y`-value. In (iii), we have a similar problem. Any vertical line drawn through the main part of the ellipse will intersect the curve twice. Again, we have `x`-values associated with more than one `y`-value. A simple geometric test to decide whether a graph represents a function is
Every vertical line may intersect the graph at most once.