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Rational Functions

This chapter explores rational functions by first defining and combining rational expressions. Then, we go over graphing and solving functions involving rational expressions. Finally, rational function inverses and transformations are manipulated.

First, a rational number is defined. This is any number that can be rewritten as a fraction of two integers. In the same way, a rational expression is a fraction where the denominator and numerator both contains polynomials. Since rational numbers and expressions are similar, many of the same rules apply.

Next, the chapter looks at rational functions which are functions that contains at least one rational expression. Depending on how they are written, these functions have one or more asymptotes which is a line that the function's graph approaches but never intercepts.

We will also discuss rational equations which are equations containing at least one rational expression. As with any equation, these can be solved both graphically and algebraically. The chapter also shows how, when solving rational equations, extraneous solutions can arise. These are solutions that do not satisfy the original equation.

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