The study of asymptotes constitutes one of the earliest and most significant encounters a high school mathematics student can have with infinity. The study of horizontal asymptotes, in particular, contributes to a student's later understanding of limits and the notion of “arbitrarily close to.” Typically, students are exposed to horizontal asymptotes in the contexts of exponential and rational functions. Real–life applications of exponential functions abound, but real–life applications of rational functions do not. In this article, we present a hands–on activity that allows students to explore horizontal asymptotes of graphs of rational functions visually and mathematically and that has been used successfully with intermediate algebra, precalculus, college algebra, and mathematics methods students.

Contributor Notes

Anna A. Davis,, is a mathematics professor at Ohio Dominican University in Columbus. She is interested in creative writing, art, and cognitive psychology.

Ronald E. Zielke,, is a mathematics professor at Ohio Dominican University, specializing in preparing preservice and in-service mathematics teachers at all levels. He is interested in project-based learning, lesson study, and mathematical selfefficacy.

Jessica L. Lickeri,, teaches developmental and introductory mathematics at Columbus State Community College. She taught for more than ten years at the secondary and postsecondary school levels.

Ronald E. Zielke; Anna A. Davis

(Corresponding author is Davis
(Corresponding author is Zielke
(Corresponding author is Lickeri
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