##
* *Reflection: Continuous Assessment
Inverse Functions - Section 3: Group Work

In the class presentation, students are presented with a definition of inverse functions verbally (“a function that undoes another), symbolically (f(f-1(x))=x), graphically, and as a relationship presented in tables of values. These multiple representations are meant to help clarify the big idea of inverse functions, but can sometimes confuse students too.

This task offers students an opportunity to develop their understanding by demonstrating all of these representations while exploring one function at a time. They must represent the inverse function in its symbolic form, identify the domain and range of both function and inverse, make a table of values for each that demonstrates inverses, and graph both functions together. By working in groups, they can self-check along the way and I can quickly assess which groups might need more assistance from me. Using a task that shows one function with its inverse demonstrated four ways, rather than four functions each with inverses represented differently, allows students to continually self-assess. Once they can envision what an inverse function might look like in one of the four representations, they can ‘translate’ this idea to another representation even if they don’t fully understand it. For example, they may be able to see that f(x) = 2x - 3 and f-1(x) = (x+3)/2 are indeed inverses, but they may need to make a table of values for each function and graph the resulting ordered pairs in order to see the relationship in its tabular and graphical representations. I find that their understanding quickly grows and solidifies.

*Using Multiple Representations*

*Continuous Assessment: Using Multiple Representations*

# Inverse Functions

Lesson 6 of 8

## Objective: SWBAT explain what an inverse function is and determine the inverse function given a one-to-one function.

Building on the warm-up activity and the Inverse Functions powerpoint presentation from the previous day's lesson, I write out the following notes on the board:

- A step-by-step process for finding the inverse of a function presented algebraically
- A process for finding the inverse of a function presented graphically
- A process for finding the inverse of a function presented numerically

In all my instruction about inverse functions, I emphasize that inverse functions are all about switching the domain and range of a function. I hope that remembering this big picture concept will help the work with inverse function feel less abstract and more manageable.

#### Resources

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#### Group Work

*40 min*

To practice the skills outlined in the notes, students work in groups to complete WS Inverse Functions. This is a collection of problems that promote flexibility in working with inverse functions. Students convert between algebraic, numeric, and graphical representations of inverse functions.

#### Resources

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#### Assignment

*10 min*

To solidify their understanding of inverse functions and how to represent them, students complete Inverse Function Homework for the night's assignment. I anticipate that this assignment will take my students about 30 minutes. I provide an answer key through Edmodo so that they can check their answers before coming to class.

#### Resources

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- LESSON 1: Modeling Proportional Relationships
- LESSON 2: Simplifying Rational Expressions
- LESSON 3: Operations with Rational Expressions
- LESSON 4: Solving Rational Equations
- LESSON 5: Quiz and Intro to Inverse Functions
- LESSON 6: Inverse Functions
- LESSON 7: Review Stations
- LESSON 8: Unit Assessment: Rational and Inverse Functions