Lesson plan

Compare the behavior of rational and linear relationships by modeling inverse and direct relationships

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 can be expressed as algebraic fractions. A function is increasing if f(b) >= f(a) when b>a. A function is decreasing if f(b) <= f(a) when b>a. Functions can be used to model many different relationships. In this task, students develop rules for linear and rational functions to model total cost and per-person cost. Students develop a linear function to model the direct relationship between the total cost of a trip and the number of attendees. They also develop a rational function to model the 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 two explicit function rules, and then to consider what happens to the total cost of the trip, as well as the per-person cost of the trip as the number of attendees increases. Students have the opportunity to compare linear and rational functions, and to develop intuitions about the asymptotic behavior of rational functions. Vocabulary: function, input, output, domain, range, fraction, average Special Materials: None