# Defining rational functions

- Author:
- Charlie Barnes, GeoGebra Team

- Topic:
- Functions

To bring this back to our original purpose, let's restate our definition of a rational function.
A

**rational function**is a function that can be expressed in the form , where is a polynomial and is a non-zero polynomial. A**polynomial function**is a function of the form where each of the s are real numbers and is a non-negative integer.## Enter an example of a rational function below.

Which of the following functions are polynomials?

Which of the following functions are rational?

State a general relationship between polynomial functions and rational functions. (Hint: think squares and rectangles.)

A key distinction between polynomial and rational functions is that, while all polynomials are continuous, not all rational functions are continuous. Plot a rational function below that has a discontinuity at .

If is a rational function with a discontinuity at , what can you conclude?