Rational Functions Review Day

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Objective

SWBAT graph rational functions and algebraically identify key aspects of the graphs of rational functions.

Big Idea

This lesson is all about helping students to solidify their skills in graphing rational equations and wrapping up the unit.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

Precalculus and Calculus

Standards

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.C.7d

(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP4

Model with mathematics.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Warm-up: review 3-2-1 assessments

10 minutes

For the first few minutes of class today, I will take some time to review the questions that students asked in yesterday’s 3-2-1 Assessment Questions. If the question pertains to horizontal asymptotes and graphing rational functions it may be answered in today’s lesson, so I plan to put those aside and address them tomorrow. If there is time, I would also like to share the things that students listed as items they’ve learned. I think it is helpful for the whole class to hear what their classmates have learned during the unit.

Application: Graphing Rational Functions

20 minutes

Conclusion: Test Review

20 minutes

As students complete the Graphing Rational Functions worksheet, I am going to quickly check it for completion. I will probably check-it-off on my clipboard and assign points right then and there. I will post the answer sheets around the room. Students can go check answers themselves.

I feel it is much more worthwhile for students to identify their own mistakes. It is important for them to learn to take responsibility to fix them. Even if I were to collect this worksheet, and score it, students would not get the feedback soon enough to help with our upcoming test.

Once students have checked and corrected their work I want them to check in with me again and get their Test Review: Rational Functions worksheet. I am hoping students will be motivated to work hard on the graphing problems earlier in the lesson, so they can use class time to complete the Test Review instead of doing it all as homework.

Homework

1 minutes

I will ask my students to continue to work through the Test Review for homework. Tomorrow, I am going to give my students ½ a class period to finish, compare answers, and formulate questions. The remainder of the class will be devoted to taking questions from students in preparation for the unit test.

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