## Inverse Functions

In this tutorial students learn how to derive the inverse of a rational one-to-one function. The students will have to understand a few key concepts to better grasp this topic.

**First**, rational functions have numerators and denominators that are both polynomials.

**Second**, an inverse function can only be created if the original function is one-to-one. One-to-one means that each x value of the function has only 1 unique y value. The vertical line test is a visual method to check to see if a function is one-to-one.

**Third**, for each point on the inverse function there exists a reversed order pair on original function. Stated another way, the domain and range values are reversed for all points on the graph for both functions.

As an example the point **(3,7)** has an **inverse** at point **(7,3)**.

Note that the **x** values are also called **domain** or **input** values.

Note that the **y** values are also called **range** or **output** values.

## Rational Function

## Inverse Function

## Graphing Tool

Click the link below open an interactive graphing calculator using the given and derived equations. The line y=x is the line of symmetry.

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