SIMPLIFYING RATIONAL

EXPRESSIONS AND

IDENTIFYING THEM AS

SHIFTS5.1.2

RATIONAL FUNCTIONS In this lesson you will learn to transform

rational functions into a form that is easier to graph without a calculator. The process is similar to writing an improper fraction as a mixed number.

MATH NOTES - RATIONAL FUNCTIONS

A rational function is one that can be expressed as a ratio of two polynomials.

Some examples: y = ,   f(x) = ,  

g(x) = ,   h(x) =

Here are some examples that are NOT rational functions: y = ,   y =

Why are they not rational functions?

MATH NOTES - SIMPLIFYING FRACTIONS

Example: Some of the trickier algebra problems require you to simplify expressions like: .

What do we do? Eliminate the x−1 term: Recall that x−1 simply means …, so we can eliminate the x in the numerator by multiplying both the top and bottom of the original fraction by x. Since x · x−1 = 1, we now have .

Eliminate the y−2 term: Now we multiply the top and bottom of the fraction by y2 to get the answer . Since the numerator and denominator have no common factors, we are done.