Lesson plan

Graph the inverse of a function by using y=x as the line of reflection

teaches Common Core State Standards CCSS.Math.Content.HSF-BF.B.4c http://corestandards.org/Math/Content/HSF/BF/B/4/c

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Big Ideas: A function maps a set of inputs (a domain) to a set of outputs (a range), and each element of the domain is related to exactly one element of the range. An inverse of a function maps the outputs back to their corresponding inputs, and hence the range of a function is the domain of the inverse. The graph of an inverse of a function is a reflection of the function across the line y=x. This task uses projectile motion as a context for students to explore the relationship between the graph of a function and the graph of its inverse. By graphing a function and its inverse on the same coordinate plane, students discover that the graph of the inverse is a reflection of the original function over the line y=x. Students also notice that for every coordinate pair (a,b) that satisfies the function, the coordinate pair (b,a) satisfies the inverse. Vocabulary: function, inverse Special Materials: Graph paper