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Copyright © 2011 Pearson, Inc. 2.6 Graphs of Rational Functions.

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Presentation on theme: "Copyright © 2011 Pearson, Inc. 2.6 Graphs of Rational Functions."— Presentation transcript:

1 Copyright © 2011 Pearson, Inc. 2.6 Graphs of Rational Functions

2 Copyright © 2011 Pearson, Inc. Slide 2.6 - 2 What you’ll learn about Rational Functions Transformations of the Reciprocal Function Limits and Asymptotes Analyzing Graphs of Rational Functions Exploring Relative Humidity … and why Rational functions are used in calculus and in scientific applications such as inverse proportions.

3 Copyright © 2011 Pearson, Inc. Slide 2.6 - 3 Rational Functions

4 Copyright © 2011 Pearson, Inc. Slide 2.6 - 4 Example Finding the Domain of a Rational Function

5 Copyright © 2011 Pearson, Inc. Slide 2.6 - 5 Example Finding the Domain of a Rational Function

6 Copyright © 2011 Pearson, Inc. Slide 2.6 - 6 The Reciprocal Function Domain: Range: Continuity: All x ≠ 0 Decreasing on Symmetric with respect to origin (an odd function) Unbounded No local extrema Horizontal asymptote: y = 0 Vertical asymptote: x = 0 End behavior:

7 Copyright © 2011 Pearson, Inc. Slide 2.6 - 7 Example Transforming the Reciprocal Function

8 Copyright © 2011 Pearson, Inc. Slide 2.6 - 8 Example Transforming the Reciprocal Function

9 Copyright © 2011 Pearson, Inc. Slide 2.6 - 9 Example Transforming the Reciprocal Function

10 Copyright © 2011 Pearson, Inc. Slide 2.6 - 10 Example Transforming the Reciprocal Function

11 Copyright © 2011 Pearson, Inc. Slide 2.6 - 11 Example Transforming the Reciprocal Function

12 Copyright © 2011 Pearson, Inc. Slide 2.6 - 12 Graph of a Rational Function

13 Copyright © 2011 Pearson, Inc. Slide 2.6 - 13 Graph of a Rational Function

14 Copyright © 2011 Pearson, Inc. Slide 2.6 - 14 Example Finding Asymptotes of Rational Functions

15 Copyright © 2011 Pearson, Inc. Slide 2.6 - 15 Example Finding Asymptotes of Rational Functions

16 Copyright © 2011 Pearson, Inc. Slide 2.6 - 16 Example Graphing a Rational Function

17 Copyright © 2011 Pearson, Inc. Slide 2.6 - 17 Example Graphing a Rational Function

18 Copyright © 2011 Pearson, Inc. Slide 2.6 - 18 Quick Review

19 Copyright © 2011 Pearson, Inc. Slide 2.6 - 19 Quick Review Solutions

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