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Graphs of Rational Functions (Lesson 2.6 Part 2)

Unit 2 Day 10
CED Topic(s): 1.8, 1.9, 1.10

​Overview

Today students will practice analyzing rational functions in a fast-paced, engaging relay race. Students will identify holes, asymptotes, and intercepts, describe them using limit notation and construct a graph based on these features.

Activity: Relay Race

     

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Lesson Handout

Answer Key

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Instructions

Prep: Print pages 2-7 in the activity file. Each group will need 1 copy. 

Play: 

  1. Divide the class into groups of 4 using any method you prefer. 

  2. Arrange each team into a vertical row with all students facing in one direction.

  3. Once the relay begins, there should be NO talking or communicating among team members.

  4. Project the rational function of the current relay so that it is visible to all team members. This will allow each team member to be planning their step while they wait for the paper to come to them.

  5. Each team member will complete one step of the relay and will then pass the paper to the person behind him/her.

  6. Papers can only be passed backward, not forward.

  7. Team members should only work on their own part of the problem and not look at or evaluate another team member’s work (except for the last person).

  8. Team assignments are:

    1.   Vertical asymptotes/holes 

    2. Limits at infinity and horizontal and slant asymptotes

    3. x- and y- intercepts

    4. Graph incorporating all features above

  9. The last person will compile all the information into a graph and will then call the teacher over to assess the result. NOTE: If there is not enough information to draw the graph, the last person is allowed to find one or two points on the graph, but only in this situation!

  10. If any team member made an error (or didn’t show complete work), the teacher will return the paper to that person for corrections and the relay will resume from that point. 

  11. The first team to correctly complete the entire relay wins that event. This ends the relay for the whole class.

  12. As a class, go over the answers to each step paying special attention to the notation. (For example: step 1 should include one-sided limits to describe the function’s behavior to the left and right of the hole or vertical asymptote.)

  13. For the next relay, have each person sitting in Seat #1 move to Seat #2, Seat #2 moves to Seat #3, Seat #3 moves to Seat #4 and Seat #4 moves to Seat #1.

  14. Repeat the process with Relays 2 – 6.

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