Graphs of Rational Functions

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Presentation transcript:

Graphs of Rational Functions 2.6 Graphs of Rational Functions

Quick Review

Quick Review Solutions

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.

Rational Functions

Asymptotes Asymptotes: Rational functions have horizontal and vertical asymptotes. Vertical Asymptotes occur where the denominator = 0. Horizontal asymptotes occur as x goes to Graph y=1/x and identify the asymptotes

Limit Notation Right Side and Left Side of Numbers

Example 1 Finding the Domain of a Rational Function

Example 2

Example 3A Finding Asymptotes of Rational Functions Look at the graph on your graphing calculator.

Graph a Rational Function

Graph a Rational Function

Example 3B Finding Asymptotes of Rational Functions Slide 2- 13

Examples using Graphing Rules

Example 5 Graphing a Rational Function

Example 6 The homework says “analyze” in #37-40. Precalculus Notes 2.6 Example 6 The homework says “analyze” in #37-40. Just do intercepts and asymptotes and sketch.

Example 4