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

Question

anonymous · Answer

The vertical line test is used to determine whether a graph is the graph of a function.  Essentially, the test amounts to answering this question: is it possible to draw a vertical line that intersects the graph in two or more places?  If so, then the graph is not the graph of a function.  If it is not possible, then the graph is the graph of a function.  Why does this test work? A graph would fail to be a function if for any input x, there existed more than one y-value corresponding to it.