- 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.
- rational function
- horizontal asymptote
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.