## asymptote explanations.pdf - Section 2: Investigation and New Learning

*asymptote explanations.pdf*

# Graphing y=a/(x-b)+c

Lesson 5 of 10

## Objective: SWBAT choose inputs to graph functions in the form y=a/(x-b)+c and identify the asymptotes of these functions using their data tables. Students will be able to write approach statements to describe the behavior of these functions near their asymptotes.

## Big Idea: Students develop the tools to graph rational functions by choosing inputs that reveal the behavior of vertical and horizontal asymptotes. Students describe this behavior using approach statements.

*70 minutes*

##### Resources (9)

#### Resources

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#### Closing

*10 min*

I use these 4 closing questions (Exit Ticket 5) differently depending on how the lesson has proceeded. Typically, I distribute the questions on a half-sheet of paper. I give students 5 minutes or so to discuss the questions with their partner or group and to attempt to answer them. Then, I facilitate a brief whole-class discussion, during with I make sure that somebody (me or a student) clearly articulates the key ideas (Exit Ticket Sample Responses).

At this time, I usually project the questions and write the key ideas on the projected copy during the discussion. I then give students a few more minutes to write their best answers to the questions. I read student responses as they leave the classroom and they can either keep their answers or give them to me.

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Introduction to Rational Functions with Real-World Applications
- LESSON 2: More Applications of Rational Functions
- LESSON 3: Graphing y=1/x
- LESSON 4: Transformations of y=1/x
- LESSON 5: Graphing y=a/(x-b)+c
- LESSON 6: Writing Approach Statements from Graphs
- LESSON 7: Matching Graph Transformations to Equations
- LESSON 8: Compare and Contrast Graphs of Rational Functions
- LESSON 9: Rational Function Review
- LESSON 10: Rational Function Summative Assessment and Portfolio