Lesson plan

Identify key features of the graph of a rational function by exploring inversely proportional relationships

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/x has a characteristic shape. When a and x are positive, f(x) is decreasingly decreasing, and the graph is a curve. As x increases, f(x) gets closer and closer to a specific value. This creates a horizontal asymptote in the graph. 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. Students use the graph to explore key features of the graph, including its domain, it maxima, whether it is increasing or decreasing, and its infinite behavior. Vocabulary: Graph, plot, point, function, asymptote Special Materials: Graph Paper