Lesson plan

Analyze the unit rates of change of translated rational functions by modeling per-person cost

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+bx)/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+bx)/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. If students have completed Task 3, it is possible to have students understand that the functions f(x)=a/x and the function g(x)=(a+bx)/x have identical unit rates of change, even though the functions may look different. This is helpful in having students understand how the value of b relates to the limit of g(x) as x goes to infinity, and the location of the horizontal asymptote on the graph of g(x). Vocabulary: table, cost, rate of change, average Special Materials: None