Lesson plan

Analyze rate of change of rational functions by exploring inverse proportions

teaches Common Core State Standards CCSS.Math.Content.HSF-IF.B.6 http://corestandards.org/Math/Content/HSF/IF/B/6

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Big Ideas: The rational function f(x)=a/x is decreasingly decreasing when a and x are positive. In this task, students explore unit rates of change for a function of the type f(x)=a/x. By modeling per-person cost as a function of people, students observe that, for every additional person, the change in per-person cost is not constant. In fact, the change in per-person cost is getting smaller and smaller. This helps build a foundational sense of the behavior of rational functions that is helpful when students begin graphing these functions and exploring asymptotic functions. Vocabulary: table, cost, rate of change, unit rate, average Special Materials: None