What does the vertical line test determine about a relation?

The vertical line test is a graphical method used to determine whether a relation is a function. According to this test, if any vertical line drawn on the graph of the relation intersects the graph at more than one point, then the relation is not a function. This is because, by definition, a function can only assign one output value (y-coordinate) to each input value (x-coordinate). If a vertical line intersects the graph at multiple points, it indicates that a single x-value is associated with multiple y-values, thereby violating the definition of a function.

This concept is critical in algebra and calculus, as understanding functions is foundational for analyzing and interpreting mathematical relationships.