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# Rational Functions

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. The numbers 0.5, .571428......., .2222.... 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 ).

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:

1) f(x) = x^3 - 2x +1/3/3x - 1

2) y = x^2 - 3x - 2/3x - 2

What does it mean to express a function in standard form? To write a function in standard form, simply replace the letter y with the function notation requested.

Sample: Express y = x^2 - 3x - 2/3x - 2 in standard form.

Since y = f(x) and f(x) = y, we can replace y with f(x).

Answer: f(x) = 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.

How to recognize a rational function?

HINT: If you see a fraction or fractions that include a variable or variables in the denominator, then you are looking at a rational function.

Sample: 90/m + 30/n = 20 is a rational function because the variables m and n appear in the denominator of both fractions.

Also, learn how to multiply and divide rational functions.

By Mr. Feliz
(c) 2005