# What is Vertical Line Test?

May 22, 2018

The vertical line test is a test that can be performed on a graph to determine if a relation is a function.

#### Explanation:

The vertical line test is a test that can be performed on a graph to determine if a relation is a function. Recall that a function can only be a function if every value of x maps to only one value of y, that is to say it's a one-to-one function or a many-to-one function.

If every value of x only has one value of y, any vertical line drawn on the graph should only intersect the graph of the function once. If this is true for any point on the graph it is said to be a function.

If you take a look at this graph you can see that any vertical line drawn will intersect the graph only once. (However horizontal lines may intersect the graph more than once)

graph{x^2 [-10, 10, -5, 5]}

An example of a relation that is not a function is ${x}^{2} + {y}^{2} = 1$

Note that this is not a function since vertical lines can be drawn that intersect the relation more than once. It is said to be a one-to-many relation or in this case actually a many-to-many relation.

graph{x^2 +y^2=1 [-10, 10, -5, 5]}