# Activities

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• • ##### Subject Area

• Math: Precalculus: Polynomial, Power, and Rational Functions

• ##### 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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Crossing the Asymptote

#### Activity Overview

This lesson involves determining when the graph of a rational function crosses its horizontal asymptote.

#### Objectives

• Students will test whether the graph of a given rational function crosses its horizontal asymptote.
• Students will examine the relationship among the coefficients of the polynomials in the numerator and denominator of various rational functions whose graph does or does not cross its asymptote.

#### Vocabulary

• rational function
• horizontal asymptote
• vertex

#### About the Lesson

This lesson involves the graph of a rational function of the form r(x) = p(x) / q(x).
As a result, students will:

• Discover conditions under which the graph of y = r(x) does or does not cross its horizontal asymptote. The functions p(x) and q(x) are assumed to be linear or quadratic polynomials.
• Manipulate graphs of rational functions and their asymptotes to determine whether they intersect.
• Make conjectures about the relationship between the coefficients of the polynomials in the numerator and denominator of a rational function whose graph does or does not cross its horizontal asymptote.