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 previously about a cylinder of fixed volume. From there, students complete a Card Sort in which they take turns matching equations and graphs of rational functions, focusing on justifying their reasoning to a partner (MP3) and making connections between the structure of the two representations (MP7).

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, the focus here is on starting to make sense of end behavior in context, with an emphasis on adapting the previously established language used to describe end behavior of polynomials to fit specific rational contexts.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.