Why does the vertical line test determine if the graph represents a function?

A function can only have one output per input. For an xy function, this means that for every x, there can only be one y. If you do the vertical line test and it crosses a line more then once, then that means that the graph has more than one y value for a single x value, meaning it is not a function.

the vertical line test is a visual way to determine if a curve is a graph of a function or not.