1 / 13

Chapter 2: Polynomial, Power, and Rational Functions

Section 2-6: Graphs of Rational Functions. Chapter 2: Polynomial, Power, and Rational Functions. Objectives. You will learn about: Rational Functions Transformations of the Reciprocal Function Limits and Asymptotes Analyzing Graphs of Rational Functions Exploring relative Humidity Why?

braith
Download Presentation

Chapter 2: Polynomial, Power, and Rational Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 2-6: Graphs of Rational Functions Chapter 2:Polynomial, Power, and Rational Functions

  2. Objectives • You will learn about: • Rational Functions • Transformations of the Reciprocal Function • Limits and Asymptotes • Analyzing Graphs of Rational Functions • Exploring relative Humidity • Why? • Rational functions are used in calculus and in scientific applications such as inverse proportions.

  3. Vocabulary • Rational function • End behavior asymptote • x-intercepts • y-intercept • Slant asymptote

  4. Rational Functions • Let f and g be polynomial functions with g(x)≠0. Then the function given by: Is a rational function

  5. Example 1Finding the Domain of a Rational Function • Find the domain of f and use limits to describe its end behavior at value(s) of x not in its domain.

  6. Example 2Transforming the Reciprocal Function • Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function. • Identify the horizontal and vertical asymptotes and use limits to describe the corresponding behavior. • Sketch the graph. • G(x)=2/(x+3) • H(x)=(3x-7)/(x-2)

  7. Example 3Finding Asymptotes • Find the horizontal and vertical asymptotes of the function. Use limits to describe the corresponding behavior of f.

  8. Graph of Rational Function

  9. Slant Asymptote • If the end behavior asymptote of a rational function is a slant line, we call it a slant asymptote.

  10. Example 4Graphing a Rational Function • Find the asymptotes and intercepts of the function and graph it.

  11. Example 5Analyzing the Graph of a Rational Function • Find the intercepts, asymptotes, and use limits to describe the behavior at the vertical asymptotes. Analyze the function and sketch the graph.

  12. Example 6Analyzing the Graph of a Rational Function • Find the intercepts, asymptotes, and use limits to describe the behavior at the vertical asymptotes. Analyze the function and sketch the graph.

  13. Examples 7 and 8 • Find the end behavior asymptote. • Analyze the function.

More Related