This Demonstration shows the vertical line test applied to the graphs of four different types of equations. As you use the horizontal slider to control the vertical line, red points appear anywhere that the line crosses the graph of the equation. If there is more than one crossing, then the graph does not pass the vertical line test, and therefore the equation does not define as a function of .

Special attention should be paid to the tangent graph's vertical asymptotes and the fact that those are not part of the graph (which is why there are no red dots shown there).