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# Stretching Exponential Functions (and your mind)

Lesson 8 of 14

## Objective: SWBAT identify a vertical stretch as equivalent to a horizontal shift with exponential functions.

## Big Idea: Students’ algebraic skills are reinforced as they discover that some different transformations are actually equivalent.

*51 minutes*

#### Homework Quiz

*10 min*

Students will spend the first 10 minutes of class today preparing for and taking their weekly Homework Quiz over worksheets #1-3 from the Exponentials unit.

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To warm-up for today’s lesson, students will review exponent rules as they complete these three clicker questions on pages 2-4 of today's Flipchart. I love using personal response systems for questions like these so I can get an accurate gauge of how many of my students actually know these exponents rules and can apply them to simplify an expression. This will help me to determine whether or not I need to review these problems in depth or if I can move my students right into the activity.

It is important that students recall the short-cut rules for adding exponents when multiplying with same bases and also multiplying exponents when taking a power to a power to be successful in today’s lesson. As students engage with these warm-up questions, they will be demonstrating **MP7** by looking for or recalling the short-cuts to exponents and making use of these properties to simplify exponential expressions.

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To wrap-up today’s learning, students should demonstrate their new knowledge by completing the questions on pages 6-7 of the Flipchart. Here students will be required to apply a deeper understanding of exponential properties by rewriting exponential functions with horizontal shifts so there is no longer that shift and it is just represented by the stretch factor. These questions will once again allow students to demonstrate **MP7** by looking for or recalling the short-cuts to exponents and making use of these properties to rewrite exponential functions.

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Hi Tiffany,

I am teaching Pre-Calculus at Gramercy Arts High School in NYC. I am enjoying using some of your lesson materials and ideas in my class, as I realized that following a text book became too dense and "ho-hum" for my students, so using the explorations in helping us work more as a community.

Since it is my first time teaching this course, I am learning alot as I go about pacing and content for the course. It would be helpful to have a key to some of these handouts, so that I could check my own work and make sure it is correct before I present it to the students. I know it can be time consuming to create these, but as you accumulate them it would be amazing if you could add them in when possible.

Thanks for all of the great lessons! I am originally from Phoenix, so finding your page made me nostalgic. I went to Maryvale High School! Maybe someday I will return and teach math at a high school there!

Best,

Karlan Judd

Teacher, Geometry and PreCalculus

Gramercy Arts High School, NY NY

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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