Vertical Line Test

What happens if you are given the graph of a relation and are asked to determine whether the graph also represents a function? You can use the vertical line test to make that determination. The vertical line test states that if every vertical line drawn through a given graph intersects the graph at no more than one point, then the graph represents a function.

Look at the following graph:

Do you think that this circle represents a function? We can use the vertical line test to make sure. Click 'Play' below to see the vertical line test performed.

When we draw a vertical line through the graph, the vertical line hits the graph in two points. This means that according to the vertical line test, this is not a function. You can use the vertical line test on all graphs to determine if the graph represents a function. Click 'Play' below to see the vertical line test performed again.

When we draw a vertical line through this graph, the vertical line hits the graph in one point. This means that according to the vertical line test, this is a function.