Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Published byEustace Stone Modified over 8 years ago

Similar presentations

Presentation on theme: "Copyright © 2011 Pearson, Inc. 2.6 Graphs of Rational Functions."— Presentation transcript:

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

2 Copyright © 2011 Pearson, Inc. Slide 2.6 - 2 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.

3 Copyright © 2011 Pearson, Inc. Slide 2.6 - 3 Rational Functions

4 Copyright © 2011 Pearson, Inc. Slide 2.6 - 4 Example Finding the Domain of a Rational Function

5 Copyright © 2011 Pearson, Inc. Slide 2.6 - 5 Example Finding the Domain of a Rational Function

6 Copyright © 2011 Pearson, Inc. Slide 2.6 - 6 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:

7 Copyright © 2011 Pearson, Inc. Slide 2.6 - 7 Example Transforming the Reciprocal Function

8 Copyright © 2011 Pearson, Inc. Slide 2.6 - 8 Example Transforming the Reciprocal Function

9 Copyright © 2011 Pearson, Inc. Slide 2.6 - 9 Example Transforming the Reciprocal Function

10 Copyright © 2011 Pearson, Inc. Slide 2.6 - 10 Example Transforming the Reciprocal Function

11 Copyright © 2011 Pearson, Inc. Slide 2.6 - 11 Example Transforming the Reciprocal Function

12 Copyright © 2011 Pearson, Inc. Slide 2.6 - 12 Graph of a Rational Function

13 Copyright © 2011 Pearson, Inc. Slide 2.6 - 13 Graph of a Rational Function

14 Copyright © 2011 Pearson, Inc. Slide 2.6 - 14 Example Finding Asymptotes of Rational Functions

15 Copyright © 2011 Pearson, Inc. Slide 2.6 - 15 Example Finding Asymptotes of Rational Functions

16 Copyright © 2011 Pearson, Inc. Slide 2.6 - 16 Example Graphing a Rational Function

17 Copyright © 2011 Pearson, Inc. Slide 2.6 - 17 Example Graphing a Rational Function

18 Copyright © 2011 Pearson, Inc. Slide 2.6 - 18 Quick Review

19 Copyright © 2011 Pearson, Inc. Slide 2.6 - 19 Quick Review Solutions

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

Similar presentations

Chapter 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant Learning Target: Learning Target: I can generate the graphs for tangent, cotangent, secant,

Chapter 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant Learning Target: Learning Target: I can generate the graphs for tangent, cotangent, secant,
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 245 Find the domain of the function f. Use limits.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 245 Find the domain of the function f. Use limits.
2.7 – Graphs of Rational Functions. By then end of today you will learn about……. Rational Functions Transformations of the Reciprocal function Limits.

2.7 – Graphs of Rational Functions. By then end of today you will learn about……. Rational Functions Transformations of the Reciprocal function Limits.
Section4.2 Rational Functions and Their Graphs. Rational Functions.

Section4.2 Rational Functions and Their Graphs. Rational Functions.
ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm

ACT Class Opener: om/coord_1213_f016.htm om/coord_1213_f016.htm
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.4 Building Functions from Functions.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.4 Building Functions from Functions.
Copyright © 2011 Pearson, Inc. 1.2 Functions and Their Properties.

Copyright © 2011 Pearson, Inc. 1.2 Functions and Their Properties.
1.5 – Analyzing Graphs of Functions

1.5 – Analyzing Graphs of Functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 234 Write the polynomial in standard form, and.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 234 Write the polynomial in standard form, and.
Copyright © 2011 Pearson, Inc. 2.3 Polynomial Functions of Higher Degree with Modeling.

Copyright © 2011 Pearson, Inc. 2.3 Polynomial Functions of Higher Degree with Modeling.
Homework, Page 223 Divide f (x) by d (x) and write a summary statement in polynomial form and fraction form 1.

Homework, Page 223 Divide f (x) by d (x) and write a summary statement in polynomial form and fraction form 1.
Determine whether a graph is symmetric with respect to the x-axis, the y-axis, and the origin. Determine whether a function is even, odd, or neither even.

Determine whether a graph is symmetric with respect to the x-axis, the y-axis, and the origin. Determine whether a function is even, odd, or neither even.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.2 Limits Involving Infinity.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.2 Limits Involving Infinity.
Copyright © 2009 Pearson Education, Inc. CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra.

Copyright © 2009 Pearson Education, Inc. CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.3 Connecting f ’ and f ” with the graph of f.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 4.3 Connecting f ’ and f ” with the graph of f.
Copyright © 2011 Pearson, Inc. 1.5 Parametric Relations and Inverses.

Copyright © 2011 Pearson, Inc. 1.5 Parametric Relations and Inverses.
Lesson 2.6 Read: Pages 146-150 Page 152: #1-37 (EOO), 47, 49, 51.

Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1.
Chapter 3 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 3.5 Rational Functions and Their Graphs.

Chapter 3 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Rational Functions and Their Graphs.
Chapter 2  2012 Pearson Education, Inc. 2.2 Limits Involving Infinity Section 2.2 Limits and Continuity.

Chapter 2  2012 Pearson Education, Inc. 2.2 Limits Involving Infinity Section 2.2 Limits and Continuity.

Similar presentations

Ads by Google