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# Multiple Representations of Exponential Functions

Lesson 5 of 11

## Objective: SWBAT switch among representations of exponential functions.

## Big Idea: Functions can be represented verbally, algebraically, numerically and graphically. Being able to switch among these representations helps us be more flexible mathematically.

*75 minutes*

#### Warm-Up

*15 min*

Log-and-Exponent-Dominoes helps my students practice with the inverse relationship between exponents and logarithms. Students work in pairs to match the dominoes from the "start" card to the "finish" card.

Like many of the hands-on activities I plan for my students, the first time I use this activity, I print the cards out on colored card stock so that they can be reused in subsequent classes.

#### Resources

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An important skill in my Algebra 2 class is the ability to translate between verbal, algebraic, graphic, and numerical representations of functions. In our study of exponential functions thus far, students have encountered algebraic and graphical representations [MP7]. In today's lesson, I introduce students to the idea of starting with a numerical representation of a function and using it it determine the algebraic form of the function.

Tables of functions Sheet1.pdf is a set of 15 input-output tables and 15 algebraic functions. The first time I use this activity with a class, I print them out on colored card stock and cut them up to create small decks of cards. Working with a partner, students match the input output table with the algebraic function. My students approach this activity in a variety of ways, so I make sure to leave time for a whole-group discussion about strategy at the end.

When students have completed the matching activity, I ask them to write about their strategy in their notebook using the following sentence starters:

- If I have an algebraic function and I want to generate a table of values, I ...
- If I have a table of values and I want to determine the algebraic function that generated the table, I ...

When everyone has a chance to complete the matching and journaling activities, I bring the whole group together for a discussion. I ask for volunteers to share their strategies and then invite other students to "build on" what has been shared [MP3].

#### Resources

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#### Independent Practice

*20 min*

In order to practice switching representations of exponential functions, my students work on WS Flexibility with Exponential Functions.docx. This is a worksheet that I created in order to help my students work flexibly with exponential functions. This worksheet asks students to switch among representations of functions and analyze features of functions.

Students will begin this work in class and complete the worksheet for homework.

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- LESSON 1: Properties of Exponents
- LESSON 2: Exponential Equations
- LESSON 3: Logarithms
- LESSON 4: Quiz and Graphing Exponential Functions
- LESSON 5: Multiple Representations of Exponential Functions
- LESSON 6: Quiz and Comparing Linear, Exponential Models
- LESSON 7: Drinking and Driving Activity
- LESSON 8: Exponential Models in the Sciences
- LESSON 9: Exponential Functions in Finance
- LESSON 10: Review Workshop: Exponential Functions and Logarithms
- LESSON 11: Unit Test: Logarithms and Exponential Functions