What is a Rational Function?

It's just a function that's also a fraction!

Numbers that can be written as fractions are called rational numbers. Here's a small list: 1/2, 4/7 and 2/9 are samples of rational numbers written as fractions. The numbers 0.5, .571428..., and .222... are all rational numbers because they are exactly the same as the fractions just listed (and the definition of rational means they can be rewritten as fractions).

Some numbers, of course, cannot be expressed as a fraction and thus they are not rational numbers. A good example of an irrational number is pi.

So then, what is a rational function? A rational function is a polynomial function divided by another polynomial function. Here is a small list of what they look like:

$$ f(x) = \frac{x^3 - 2x + 3}{3x - 1} $$ $$ y = \frac{x^2 - 3x - 2}{3x - 2} $$

The general form for rational functions looks like this: f(x) = h(x)/g(x). This general form simply means that a rational function equals the ratio one polynomial function divided by another polynomial function.

Also, learn how to multiply and divide rational functions.