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

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Presentation transcript:

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

Copyright © 2011 Pearson, Inc. Slide 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.

Copyright © 2011 Pearson, Inc. Slide Rational Functions

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

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

Copyright © 2011 Pearson, Inc. Slide 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:

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

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

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

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

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

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

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

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

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

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

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

Copyright © 2011 Pearson, Inc. Slide Quick Review

Copyright © 2011 Pearson, Inc. Slide Quick Review Solutions

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