1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 2 Polynomial, Power, and Rational Functions

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2.7 Graphs of Rational Functions

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 4 Quick Review

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 5 What you’ll learn about Rational Functions Transformations of the Reciprocal Function Limits and Asymptotes Analyzing Graphs of Rational Functions … and why Rational functions are used in calculus and in scientific applications such as inverse proportions.

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 6 Rational Functions

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 7 Finding the Domain of a Rational Function Describe the end behavior using limit notation.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 8 Viewing the Table

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 9 Finding the Domain of a Rational Function

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 10 Is the function continuous?

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13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Reciprocal Function Slide 2- 13

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 14 can be obtained through transformations of the graph of the reciprocal function. If the degree of the numerator is greater than or equal to the degree of the denominator, we can use polynomial division to rewrite the rational function. Transformations of the Reciprocal Function The graph of any nonzero rational function of the form

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Transformations of the Reciprocal Function Slide 2- 15 Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f (x)= 1/x. Identify the horizontal and vertical asymptotes and use limits to describe the corresponding behavior. Sketch the graph of the function.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 16

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18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 18 Graph a Rational Function

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 19 Graph a Rational Function

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 20 Finding Asymptotes of Rational Functions

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 21 Finding Asymptotes of Rational Functions

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 22 Finding Asymptotes of Rational Functions

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 23 Graphing a Rational Function

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Graphing a Rational Function Slide 2- 24

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27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Analyzing Graphs of Rational Functions Slide 2- 27 Find the intercepts, asymptotes, use limits to describe the behavior at the vertical asymptotes, and analyze and draw the graph of the rational function

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29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Analyzing Graphs of Rational Functions Slide 2- 29

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Finding an End-Behavior Asymptote Slide 2- 30 Find the end-behavior asymptote of and graph it together with f in two windows:

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 31 Pg. 246,#1-67 e.o.o.

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2.8 Solving Equations in One Variable