Education Technology

Exploring Vertical Asymptotes

Published on 04/11/2011

Activity Overview

This lesson involves observing how changing the values in a rational function affects the continuity of the graph of the function.

Objectives

  • Students will determine the domain of rational functions.
  • Students will use algebraic concepts to determine the vertical asymptotes of a rational function.
  • Students will determine the removable discontinuities of a rational function.
  • Students will describe the graph of a rational function given the equation.
  • Students will use appropriate tools strategically (CCSS Mathematical Practice).

Vocabulary

  • rational function
  • domain
  • asymptote
  • factors
  • zeros
  • removable discontinuity

About the Lesson

This lesson involves observing how changing the values in a rational function affects the continuity of the graph of the function.
As a result, students will:

  • Manipulate the factors of the numerator and denominator to observe the effects of each value.
  • Explain how the values in a rational function determine the vertical asymptotes.
  • Identify the conditions that must be met for a rational function to have removable discontinuity.