# 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, the inverse is not a function because it doesn’t pass the vertical line test.

So here’s the deal!

**If the horizontal line intersects the graph of a function in all places at exactly one point, then the given function should have an inverse that is also a function. We say this function passes the horizontal line test.**

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

## Horizontal Line Cutting or Hitting the Graph at Exactly One Point

- Graph of the line
*f*(*x*) = â€“*x*+2

- Graph of the square root function f\left( x \right) = \sqrt {x + 1}

- Graph of the rational function f\left( x \right) = {1 \over {x + 1}}.

On the other hand, if the horizontal line can intersect the graph of a function in some places at **more than one point**, then the function involved can’t have an inverse that is also a function.

We say this function fails the horizontal line test.

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

## Horizontal Line Cutting or Hitting the Graph at More Than One Point

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

- Graph of absolute value function f\left( x \right) = \left| x \right|

- Graph of semi-circle f\left( x \right) = \sqrt {7 - {x^2}}

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