Final answer:
If any vertical line intersects a graph more than once, the graph does not define y as a function of x.
Step-by-step explanation:
If any vertical line intersects a graph more than once, the graph does not define y as a function of x.
This is because for a relation to be a function, each input value (x) must correspond to exactly one output value (y). However, a vertical line intersects a graph at multiple points, indicating that there are multiple y-values for a single x-value, thus violating the definition of a function.
For example, consider the graph of a circle. A vertical line intersects the circle at two points, indicating that there are two y-values for a single x-value, making it not a function.