Lesson plan

Investigate invertible functions by comparing and contrasting one-to-one and many-to-one relationships

teaches Common Core State Standards CCSS.Math.Content.HSF-BF.B.4 http://corestandards.org/Math/Content/HSF/BF/B/4
teaches Common Core State Standards CCSS.Math.Content.HSF-BF.B.5 http://corestandards.org/Math/Content/HSF/BF/B/5

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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. Because of this, only functions that are one-to-one (where each element of the range is uniquely associated with an element of domain) are invertible. This lesson builds on the idea of a one-to-one function, which was introduced in Task 1: Determine if a function is one-to-one by examining the height and velocity of a projectile. In this task, students discover why a function must be one-to-one in order to be invertible by investigating a simple projectile motion model. Vocabulary: function, inverse, horizontal line test