Education Technology

Precalculus: Crossing the Asymptote
by Texas Instruments

Updated on July 01, 2014

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.