Education Technology

Evaluating Rational Functions

Published on 06/09/2008

Activity Overview

In this activity, students study the asymptotic behavior of rational functions. They explore the two types of asymptotes and make generalizations as to when they do or do not occur.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 31 - 39 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Enter the function and find factors of numerator and denominator
  • Express f(x) in factored form and record it in the space provided
  • Find and record the zeros of each factor
  • Find and record, the y-intercept of the function by evaluating it at 0
  • Use the limit command to determine the behavior of f(x) as x approaches each zero of the denominator
  • Investigate the y-value to the right (positive value) and left (negative value) of zero
  • Record the vertical asymptotes in the table
  • Use the limit command to determine the behavior of f(x) as x approaches both positive and negative infinity, and record the values
  • Find and write the horizontal asymptote
  • Sketch the graph (vertical and horizontal asymptotes) based on the information on the grid provided.
  • Confirm the graph by graphing the function on the calculator
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary