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# Graphing Exponential Functions

Lesson 10 of 13

## Objective: SWBAT graph an exponential function and identify the domain, range, horizontal asymptote, continuity, the x intercept, and the y intercept.

## Big Idea: In this lesson, the students should recognize how the vocabulary of graphing translates from a linear function to an exponential function.

*50 minutes*

#### Warm Up

*10 min*

The goal of this Warm Up is for students to review graphing vocabulary, and be able to apply it to exponential functions. Many of my students recall that a y-intercept is where a graph crosses the y axis, but they cannot find the y-intercept of an exponential function. So, in this Warm Up and in this lesson, I want students to be able to define and apply the graphing vocabulary to both a linear functions and an exponential functions.

I provide students about 10 minutes to complete the Warm Up and for us to review as a class. Visuals are important in this lesson. I review the Warm Up below in the video.

#### Resources

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I use the PowerPoint to provide students with notes and examples to demonstrate the importance of learning the structure of the exponential functions. I emphasize how the graphing vocabulary applies to linear functions, exponential functions, and how this structure will be similar throughout all functions. I also model different ways to write domain and range using inequalities and interval notation.

I provide all students with a copy of the PowerPoint in a format that provides space for notes. I demonstrate reviewing the PowerPoint below in the two videos, page 1 and page 2. I also show students all of the transformations of the base function on one Screen of the TI-Nspire, so that students will have a visual of how it shifted from the original function.

Page 1

Page 2

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#### Exit Slip

*10 min*

I use this Exit slip as a quick formative assessment during the last 10 minutes of class to complete. It helps me to quickly see what graphs students are struggling with, or which graphs that will not be necessary to reteach. I am particularly interested in determining how well my students understand the shifts, especially the equations that had more than one translation.

I have posted a key for the exit slip in the resources.

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: A Penny or $100,000!
- LESSON 2: Explore the Rebound Height of A Ball
- LESSON 3: Arithmetic vs. Geometric Sequences
- LESSON 4: Linear, Exponential, or Quadratic?
- LESSON 5: The Product Rule and the Power of Product Rule of Exponents
- LESSON 6: The Quotient Rule of Exponents and Negative Exponents
- LESSON 7: The Power of the Power Rules in Exponential Expressions
- LESSON 8: Comparing Investments
- LESSON 9: Applications of Exponential Functions and Hot Cocoa!
- LESSON 10: Graphing Exponential Functions
- LESSON 11: Assessment: Presentation on Exponential Functions, Day 1 of 2
- LESSON 12: Assessment: Presentation on Exponential Functions Day 2 of 2
- LESSON 13: Scientific Notation Is An Exponential Expression