Reviewing Rational Expressions

Definitions and Overview

Rational expressions are the quotient of two polynomials.
The asymptote is a thing (not necessarily linear) that “guides” or “blocks” the curve towards its end behavior.
Rational functions are in the form of \(\frac{P(x)}{Q(x)}\) where \(P(x)\text{ and }Q(x)\) are any function (this unit only focuses on polynomial functions though).
Recipricals are known as multiplicative inverses. Given \(y = f(x)\), the reciprocal would be \(y = \frac{1}{f(x)}\). There are some restrictions, for example, zero can not have a reciprocal (the reciprocal of zero is undefined).

Restrictions

Given \(\frac{a}{b}\), there should be a restriction for \(b\neq 0\). When \(\frac{a}{b}\div\frac{c}{d}\), \(b, c, d\neq 0\)

General Tips

• Factor first
• Keep track of restrictions
• Reduce when possible (while keeping track of restrictions)
• When graphing, draw smooth curves, not straight lines or Cusp curves

  Operations

  Make sure to keep restrictions when multiplying and dividing. When adding and subtracting, make sure to get a common denominator first.