Precalculus: Exploring Vertical Asymptotes

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.

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.