Lesson plan

# Identify key features of the graph of a translated rational function by exploring how per-person cost changes as the number of people increase

teaches Common Core State Standards CCSS.Math.Content.HSF-IF.C.7d http://corestandards.org/Math/Content/HSF/IF/C/7/d

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Big Ideas: The graph of f(x)=(a+bx)/x has a characteristic shape. When a and x are positive, f(x) is decreasingly decreasing, and the graph is a curve. The graph of f(x) has a horizontal asymptote at y=b. In this task, students create and graph a rational function that relates the number of people attending an end of the year trip, to the cost per person of the trip. This task builds on task 5 by introducing an additional parameter: in addition to the cost of the bus, each student must also contribute \$20 for gas. This creates a rational function of the form f(x)=(a+bx)/x. Students use the graph to explore key features of the graph, including its maximum, whether it is increasing or decreasing, and its infinite behavior. Vocabulary: graph, plot, point, function, asymptote Special Materials: Graph paper