IM 2.17: Graphs of Rational Functions (Part 1)

The purpose of this lesson is to introduce students to vertical asymptotes. The line  is a vertical asymptote for a rational function  if  is undefined at  and its outputs get larger and larger in the negative or positive direction when  gets closer and closer to  on each side of the line. Students begin by reasoning about a vertical asymptote of a simple rational function that represents the relationship between the time and speed needed to travel a fixed distance, building on the work they did in the previous lesson around a cylinder of fixed volume. From there, students complete a card sort in which they match equations and graphs of rational functions, focusing on making connections between the structure of the two representations (MP7) and analyzing representations and structures closely (MP2). While the end behavior of rational functions is touched on here as part of making sense of a context, the following lesson investigates end behavior and horizontal asymptotes in more depth. As such, only a light touch is needed on these ideas in this lesson, with an emphasis on adapting the previously established language around end behavior of polynomials to fit specific rational contexts.

By Algebra two