Question

Explain why the vertical line test is used to determine if a graph represents a function

Answer 1

In order for a relation to be a function, it must be well defined. That means for each input, there can only be one possible output. If you draw a vertical line through the graph of some relation and it intersects at two or more points, you've found more than one y-value (output) for the same x-value (input), so it can't be a function.