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# Rationalized Transformations: Shifting Rational Functions

Lesson 6 of 12

## Objective: SWBAT simplify complicated radical expressions to graph the function as a shift of y=1/x.

## Big Idea: Fluency with manipulating algebraic fractions improves as students investigate the transformations of various rational equations.

*51 minutes*

#### Warm-up: Homework Quiz

*10 min*

For the first 8-10 minutes of class today students I will have students complete their Homework Quiz over Homeworks #1-3 from last week.

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To help students wrap-up today’s learning and demonstrate their current understandings, I have students answer the Clicker Questions questions on page 13-15 of today’s Flipchart. The question on page 13 assesses today’s new learnings, while giving students an opportunity to apply the new vocabulary word, asymptote. The questions on page 14-15 are a stretched version of the parent function. For the question on page 14, I plan to just have students answer it based on their knowledge of asymptotes and shifting. Then, I will talk a bit about the stretch factor of 2. For the next question, I will encourage students to use their knowledge of shifting to eliminate some answers. Answers 1 and 4 will probably both appear correct to students as they both have the correct shift. Then, I will encourage students to use a test point to find the correct answer. Testing when x=2 works great!

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#### Homework

*1 min*

I plan to assign Homework 4 - Rational Functions for the students to begin working on this evening.

#### Resources

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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: Rational Approaches to Solving Rational Equations
- LESSON 2: Speed Dating Rationally
- LESSON 3: Another Rational Approach to Solving: Graphing
- LESSON 4: Ahoy again! What can you see now? Building Rational Functions
- LESSON 5: Evolving Rational Functions
- LESSON 6: Rationalized Transformations: Shifting Rational Functions
- LESSON 7: Light it Up - Day 1: Modeling with Rational Functions
- LESSON 8: Light it Up – Day 2: Modeling with Rational Functions
- LESSON 9: You can’t Get There from Here: Finding the Asymptotes
- LESSON 10: Rational Functions Review Day
- LESSON 11: Rational Functions Test Review
- LESSON 12: Rational Functions and Equations Test