Question

what is a vertical line test

Answer 1

The vertical line test is a method used in mathematics, particularly in the study of relations and functions, to determine whether a given curve or graph represents a function. According to the test, if a vertical line intersects a graph more than once at any point, then the graph does not represent a function. This is because, for a relation to be a function, each input (or x-value) must be related to exactly one output (or y-value).

In practice, you can apply the vertical line test by imagining a vertical line drawn anywhere along the x-axis. If the line crosses the graph at more than one point, it indicates that a single x-value corresponds to multiple y-values, violating the definition of a function. If the vertical line intersects the graph at most once, the graph represents a valid function.