In this lesson, students continue their investigation connecting features of graphs and equations of rational functions with the focus now on horizontal asymptotes as a type of end behavior. The line \(y=c\) is a horizontal asymptote for \(f\) if \(f(x)\) gets closer and closer to \(c\) as the magnitude of \(x\) increases.
Students begin the lesson considering a common error when rewriting fractions, in preparation for rewriting fractions themselves. Next, they reason about the average cost to produce \(x\) number of books, first making sense of a nonzero horizontal asymptote in context, and then by rewriting the original expression (MP2). In the following activity, students match equations to graphs of rational functions with an emphasis on rewriting as needed to make the match.
In the following lesson, students will more formally address how to use polynomial long division to rewrite rational functions of the form \(\frac{a(x)}{b(x)}\) as \(q(x) + \frac{r(x)}{b(x)}\), where \(a(x)\), \(b(x)\), \(q(x)\), and \(r(x)\) are all polynomials and \(b(x) \neq 0\). For this lesson, students are expected to take a more informal approach, rewriting by inspection and applying their knowledge of fractions.
Lesson overview
 18.1 Warmup: Rewritten Equations (5 minutes)
 18.2 Activity: Publishing a Paperback (15 minutes)

18.3 Activity: Horizontal Asymptotes (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 18.4 Cooldown: Publishing a Paperback, Revisited (5 minutes)
Learning goals:
 Identify horizontal asymptotes of simple rational functions from their equations.
 Interpret a graph of a rational function and explain the meaning of the horizontal asymptote in context.
Learning goals (student facing):
 Let’s learn about horizontal asymptotes.
Learning targets (student facing):
 I can identify a horizontal asymptote from a graph or an equation of a rational function.
Glossary:
 horizontal asymptote  The line \(y =c\) is a horizontal asymptote of a function if the outputs of the function get closer and closer to \(c\) as the inputs get larger and larger in either the positive or negative direction. This means the graph gets closer and closer to the line as you move to the right or left along the \(x\)axis.
 Access the complete Algebra 2 Course glossary.
Standards:
 This lesson builds towards the standard: CCSS.HSAAPR.D.6MS.AAPR.6MO.A2.APR.A.4
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