# Activities

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• • ##### Subject Area

• Math: Algebra II: Rational Expressions

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.6

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Graphs of Rational Functions

#### Activity Overview

Investigate the graphs of rational functions.

#### Objectives

• Students will determine the domain and range of a rational function.
• Students will describe the end behavior and the graph of a rational function near its asymptote.
• Students will connect the horizontal translation of a graph of a rational function to its equation.
• Students will find the equations of a rational function with specified asymptote(s) or restriction(s).

#### Vocabulary

• end behavior
• rational function
• asymptote
• horizontal shift
• positive or negative infinity
• domain and range

#### About the Lesson

This lesson involves investigating the graphs of rational functions. As a result, students will:

• Describe the end behavior of the graph of f(x)=1/x and what is happening near the asymptote.
• Horizontally translate the graph of f(x)=1/x and determine the relationship between the equation of the asymptote and the equation of the rational function.
• Write the equations of graphs of rational functions with two asymptotes.