Section 3.5 Rational Functions and Their Graphs

Rational Functions

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

Graphing Calculator Connected mode Dot Mode

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

Example

Graphing Rational Functions

Example

Example

Slant Asymptotes

Example

Example

Applications

Example The Fort Myers Fishing Company discovered a better material for making fishing reels. The fixed monthly cost is $10,000 for the cost of rental of space, manufacturing equipment, as well as wages and benefits for it’s employees. It costs $10 for materials to make each fishing reel.

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

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

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