Section 3.5 Rational Functions and Their Graphs

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Presentation transcript:

Section 3.5 Rational Functions and Their Graphs

Example Find the domain of the rational function.

Example Find the domain of the rational function.

Vertical Asymptotes of Rational Functions

Two Graphs with Vertical Asymptotes, one without

Example Find the vertical asymptote, if any, of the graph of the rational function.

Example Find the vertical asymptote, if any, of the graph of the rational function.

Example Find the vertical asymptote, if any, of the graph of the rational function.

A graph with a hole corresponding to the denominator’s zero A graph with a hole corresponding to the denominator’s zero. Your calculator will not show the hole.

Horizontal Asymptotes of Rational Functions

Two Graphs with Horizontal Asymptotes, one without Notice how the horizontal asymptote intersects the graph.

Example Find the horizontal asymptote, if any, of the graph of the rational function.

Example Find the horizontal asymptote, if any, of the graph of the rational function.

Using Transformations to Graph Rational Functions

Graphs of Common Rational Functions

Transformations of Rational Functions

Example

Graphing Rational Functions

Example

Example

Slant Asymptotes

Example

Example

Applications

(a) (b) (c) (d)

(a) (b) (c) (d)

(a) (b) (c) (d)