Lesson plan

Build a rational function by modeling an inversely proportional relationship

teaches Common Core State Standards CCSS.Math.Content.HSF-BF.A.1 http://corestandards.org/Math/Content/HSF/BF/A/1

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Big Ideas: Rational functions are expressed as algebraic fractions. In an inverse proportion, as the magnitude of the independent variable increases, the magnitude of the dependent variable decreases, and their product stays the same. Rational functions can be used to model many different relationships. In this task, students develop a rational function to model the inverse relationship between the per-person cost of a trip and the number of attendees. Students are encouraged to use a table of values to create an explicit function rule, and then to consider what happens to the per-person cost of the trip as the number of attendees increases. In this way, students have the opportunity to develop intuitions about the asymptotic behavior of rational functions. Vocabulary: function, input, output, domain, range, fraction, average Special Materials: None