Rational functions are quotients or fractions of polynomials.

(Note: Polynomials are rational functions, since they can be written in fraction form with \(1\) as the denominator and \(1\) is a polynomial.)

So, it is not surprising that analyzing rational functions follows the same plan as for polynomials.

Analyzing a rational functions follows the same process as analyzing polynomials. The difference comes for zeros of the polynomial in the denominator. Since these are in the denominator, they are singularities for the whole rational function.

• Domain
• Zeros

• Continuity

  • discontinuities
  • singularities
• End-Behavior

• Behavior

  • intervals where increasing
  • intervals where decreasing
• Global Maximum and Minimum
• Local Maximums and Minimums
• Range
• ...and we would like a nice graph

Learning Outcomes

In this section, students will

• analyze rational functions.