Horizontal Line Test

In this lesson, we will learn about one-to-one functions and how to determine if a function is one-to-one using the horizontal line test. We already know that a function is a special type of relation where for each x-value there is one and only one y-value. With a one-to-one function, we can also say that for each y-value there is one and only one x-value. So for each x, there is one y and for each y, there is one x. A horizontal line of the form y = k, can be used to determine if a function is one-to-one. For each point on a horizontal line, the y-value is the same, so if any horizontal line impacts the graph in more than one location, this tells us that the given y-value is associated with more than one x-value and is not a one-to-one function.