**Horizontal Line Test**

The **horizontal line test** is a convenient method that can determine whether a given function has an inverse, but more importantly to find out if the inverse is also a function.

Remember that it is very possible that a function may have an inverse but at the same time not a function, because it doesn’t pass the vertical line test.

So these are the rules:

Here are some examples of functions that **pass** the horizontal line test:

## Horizontal Line Cutting the Graph at Exactly One Point

- Graph of the line
*f*(*x*) = –*x*+2

- Graph of the square root function

- Graph of the rational function

Here are some examples of functions that **fail** the horizontal line test:

## Horizontal Line Cutting the Graph in More Than One Point

- Graph of the parabola
*f*(*x*) =*x*^{2}– 2

- Graph of absolute value function

- Graph of semi-circle