## MP8.MP4 - Section 3: Graphing Exponentials

# Graphing Exponential Functions

Lesson 3 of 14

## Objective: SWBAT graph exponential functions showing intercepts and end behaviors, show key features of a graph, and review using function notation to evaluate functions for inputs in their domains.

## Big Idea: Using tables to graph exponential functions, students explore exponential growth & decay while idenitfying properties such as domain, range, & asymptotes.

*50 minutes*

#### Vocabulary

*1 min*

Present page 5 of the flipchart to formally define exponential functions for students. They should add this to their Personal Dictionaries in their own words.

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#### Graphing Exponentials

*40 min*

Students should work through the *Graphing Basic Exponential Functions *handout. It is essential that all students work through question 12 to master the learning targets for today. Question 13 is more of an extension and those ideas will also be established later in this unit if students run out of time today. This activity could be completed individually by students or in teams. I will not be allowing the use of a graphing calculator for this activity.

As students are working though this activity I will be looking for them to demonstrate **Mathematical Practice 6: attending to precision. **I will specifically be checking each students graphs as I monitor the classroom to be sure that none of their graphs dip below the x-axis.

Another important practice I will be informally assessing as students work is their ability to apply **Mathematical Practice 8: Look for and express regularity in repeated reasoning. **I want to see students not only apply their exponent rules and tables to graph the functions, but be able to use the patterns and the their reasoning skills to conclude that exponential functions will never be equal to zero but will continue to get closer and closer to zero as x decreases in growth functions (or increases in a decay functions). Students understandings of this concept will be demonstrated in questions 1 and 4.

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#### Closure

*5 min*

The closure questions today (pages 6-10 of the flipchart) assess students’ knowledge of identifying exponential growth and decay functions. Students should be able to match the graphs on the last two pages by simply using their knowledge of growth and decay functions.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Cat Island (Day 1 of 2): Cats can’t add but they do multiply!
- LESSON 2: Cat Island (Day 2 of 2): Cats can’t add but they do multiply!
- LESSON 3: Graphing Exponential Functions
- LESSON 4: Shifting Exponential Functions
- LESSON 5: Counting the Change: Linear, quadratic, or exponential? (Day 1 of 2)
- LESSON 6: Counting the Change: Linear, quadratic, or exponential? (Day 2 of 2)
- LESSON 7: Sorting out the Change
- LESSON 8: Stretching Exponential Functions (and your mind)
- LESSON 9: Credit Card Investigation: What is interest? (Day 1 of 4)
- LESSON 10: Credit Card Investigation: What is interest? (Day 2 of 4)
- LESSON 11: Credit Cards Investigation: How is interest really calculated? (Day 3 of 4)
- LESSON 12: Credit Card Investigation: A Dastardly Scheme (Day 4 of 4)
- LESSON 13: Exponential Functions Test Review
- LESSON 14: Exponentials Functions Unit Test