## Reflections, Stretches, and Shrinks- Absolute Value Functions Day 1 - Section 4: Reflections, Stretches, and Shrinks of Absolute Value Functions

*Reflections, Stretches, and Shrinks- Absolute Value Functions Day 1*

*Reflections, Stretches, and Shrinks- Absolute Value Functions Day 1*

# Absolute Value Functions: Transformations Day 1

Lesson 20 of 24

## Objective: Students will be able to graph transformations of absolute value functions.

#### Warm up and Homework Check

*10 min*

I include **Warm ups **with a **Rubric **as part of my daily routine. My goal is to allow students to work on **Math Practice 3 **each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Absolute Value Functions Day 1 asks students to create their own questions from a scenario.

I also use this time to correct and record the previous day's Homework.

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This is the first day of a two-day lesson. I have included the entire (2-day) PowerPoint, (with two separate exit tickets) as an option if the first day goes faster than expected. This way you can simply continue to as far as your class gets.

This lesson begins with a simple scenario. *The average monthly temperature for January in a northern Canadian city is 0 degrees Fahrenheit.* I ask the students to create a chart that shows the difference between a set of daily temperatures and the average and then graph this information. We discuss the function that models this distance (**Math Practice 4**). The purpose of this short activity is to allow the students to recall their conceptual knowledge of absolute value and connect it to its graph on a coordinate plane.

This is an appropriate time to discuss the shape of the absolute value graph. Why does it have a “v” shape? How does it relate to f(x)=x? I ask the class some leading questions to get a class discussion.

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Today’s lesson is my students’ first experience with transformation of functions. We revisit this concept repeatedly in subsequent units for each separate parent function. We begin with first vertical and then horizontal Translations. My students use graphing calculators to explore each one (**Math Practice 5**) and then write a statement generalizing how each affects the parent function (**Math Practice 7**). We then discuss these statements as a class. For horizontal translations, I ask my students why these move opposite to the sign in the equation. This is a good place to use a think-pair-share. It may be a good idea here to rewrite the function like: f(x) – c = abs(x – b). This may help the students reason out why the horizontal translation goes opposite while the vertical translation doesn't seem to.

Please see the PowerPoint for detailed presentation notes.

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My students perform a similar procedure as in the last section for Reflections, Stretches, and Shrinks. We start with the reflection f(x) = -abs(x). I have also included the function f(x) = abs(-x). I ask them to predict the transformation given the previous reflection. Some may be surprised at the result. This is a great place to do a think-pair-share on why the graph didn’t seem to change (**Math Practice 2**).

Now the students look at stretches. This should be run similarly to the translations. The only difference is that the students need both a general and specific knowledge of what is happening. Generally, they should know that the bigger the number, the narrower the graph. More specifically, they should know that when something is multiplied by a four, it is four times taller. I have them investigate and then write a general statement about this.

Once they have a decent idea of stretches, I introduce shrinks. This throws a kink into the statement they just wrote. This is a great example of the need for precision (**Math Practice 6**). I have them rewrite their generalization with this new information. At this point, I ask for a volunteer to share theirs as a working model. The students analyze this definition for completeness. If the students are feeling lost, I ask a guiding question like: “Does this clear about what happens with both numbers bigger than one and numbers smaller than one?”, or “Is it enough to say a number smaller than one?”

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

This Exit Ticket asks students to write and graph a function that uses two of the transformations that they have learned.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Mathematical Modeling: Properties of Functions Day 1 of 2
- LESSON 2: Mathematical Modeling: Properties of Functions Day 2 of 2
- LESSON 3: Mathematical Modeling: Linear Functions
- LESSON 4: Mathematical Modeling: Linear Functions Design Project
- LESSON 5: Finding Equations of Parallel and Perpendicular Lines
- LESSON 6: Inverse Functions
- LESSON 7: System of Equations Day 1 of 2
- LESSON 8: Systems of Equations Day 2 of 2
- LESSON 9: Modeling Systems of Equations
- LESSON 10: Function Review
- LESSON 11: Function Mid Test
- LESSON 12: The Tortoise and The Hare Project Day 1
- LESSON 13: The Tortoise and The Hare Project Day 2
- LESSON 14: The Tortoise and The Hare Project Day 3
- LESSON 15: The Tortoise and the Hare Project Day 4
- LESSON 16: The Tortoise and the Hare Piece-wise Functions
- LESSON 17: Step Functions
- LESSON 18: Absolute Value Equations
- LESSON 19: Absolute Value Inequalities
- LESSON 20: Absolute Value Functions: Transformations Day 1
- LESSON 21: Absolute Value Functions: Transformations Day 2
- LESSON 22: Functions Test Review Day 1
- LESSON 23: Functions Test Review Day 2
- LESSON 24: Functions Test