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# Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions

Lesson 7 of 21

## Objective: Students will learn that just as numbers can be combined through arithmetic operations, functions can also be combined through a process known as composition. Through this lens, inverse functions will be developed and extended to exponential functions.

#### Beginning

*7 min*

The “welcome back” from spring break can often be a drag for both students and teachers! To start class, I enjoy finding out what exciting things my students did over spring break. I have found that if I do not give them an opportunity to share out, that they usually lack focus and end up sharing out anyways! This is just another way to take 5 minutes to build positive relationships with your students. I use **www.polleverywhere.com** to share out for the simple fact that it gets my students on the website that we will use for a future activity. As a teacher, all you have to do is hit “Clear Results” and it will be refreshed for the next question. It is a great feature!

As more of a “mathematical focused” lesson beginning, I pass out mini whiteboard to the students as we talk about their spring break activities and travels. My whiteboards also have a graph grid on the opposite side – a great buy if your school is looking for a solid educational investment. I have also known teachers who have cut up shower board from the lumber yard for their whiteboards. This is equally as effective, and cuts cost.

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#### Exit Slip

*5 min*

This Exit Slip is a neat way to get the students thinking about the inverses of exponential functions. The students should be able to recognize that the exponential graphs that we have looked at (in the lessons before spring break) will have inverses. They should also be more familiar with the mathematical reason WHY this is the case… not simply because they pass the horizontal line test. Without even knowing it, the students will have plotted their first logarithmic function, specifically . This is really exciting, and makes for a great starting point in future lessons! Plus, now that we know the inverse, we can MAKE USE OF STRUCTURE to mathematically solve a new realm of exponential equations. We have discovered and established the structure – now in the upcoming lessons we get to play around with it!

#### Resources

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Introduction to Exponential Functions - Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: A Conceptual Introduction to Exponential Functions: Collaboration, Questioning, and Financial Advice!
- LESSON 4: Discovering Solutions to Exponential Equations
- LESSON 5: An "Exponentially" Rewarding Battle!
- LESSON 6: Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions
- LESSON 7: Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions
- LESSON 8: Exponential Functions and Logarithms - Connecting the Dots
- LESSON 9: Exponentials and Logarithms: LOUD and CLEAR!
- LESSON 10: A Wrap on Logarithmic dB's and An Extension to Logarithmic Properties
- LESSON 11: Classroom Journey: Exponential and Logarithmic Properties
- LESSON 12: Laws of Logarithms and Real Applications
- LESSON 13: Calculator Boot-Camp and Solving Exponential Equations
- LESSON 14: Logs, Loans, and Life Lessons!
- LESSON 15: "Demystifying e" Day #1
- LESSON 16: Logs, Loans, and Life Lessons Collaboration Day!
- LESSON 17: FInal Discussion - "Demystifying e" PLUS Skills Practice with Logarithms
- LESSON 18: Elephant Tracks!
- LESSON 19: End of Unit Differentiated Problem Set
- LESSON 20: Differentiated Problem Share Out - Unit Review
- LESSON 21: Unit Review