In this lesson, students continue to expand their capacity to work with and interpret inverses of linear functions in various situations. Previously, students found inverses of functions that were defined using two variables. Here, they find inverses of functions given in function notation.
In earlier lessons, students worked with functions in which the quantities and the relationship between them were straightforward and well defined. In this lesson, students still engage with such functions, but they also work with a relationship that is less well defined. In the last activity, students analyze a data set, write a linear function to model the data, and use the model (including writing an equation that represents the inverse function) to solve problems. Along the way, students engage with different aspects of modeling (MP4).
Note that notation of the form \(f^{\text1}\) is intentionally not used to denote inverse function at this point. This is so that students can focus their attention on the meaning of an inverse function rather than on learning a new notation. It is also to discourage students from thinking of finding an inverse function as a procedure.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. Consider making technology available.
Lesson overview
 17.1 Warmup: Water in a Tank (5 minutes)
 17.2 Activity: Another Look at the Tank (10 minutes)

17.3 Activity: Phones in Homes (20 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 17.4 Cooldown: Time on the Trail (5 minutes)
Learning goals:
 Find the inverse of a linear function given in function notation.
 Write a linear function and an inverse function to model data and solve problems.
Learning goals (student facing):

Let’s use inverse functions to solve problems.
Learning targets (student facing):
 I can write a linear function to model given data and find the inverse of the function.
 When given a linear function defined using function notation, I know how to find its inverse.
Standards:
 This lesson builds on the standard:CCSS.HSFIF.B.6MS.FIF.6MO.A1.IF.B.5
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