Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L...

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Rational Functions and their graphs 1 November 06, 2018 Rational Functions and Their Graphs Objectives: • Find the domains of rational functions. • Use arrow notation. • Identify vertical asymptotes. • Identify horizontal asymptotes. • Use transformations to graph rational functions. • Graph rational functions. • Identify slant asymptotes. • Solve applied problems involving rational functions.

Transcript of Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L...

Page 1: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

Rational Functions and their graphs

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November 06, 2018

Rational Functions and Their Graphs

Objectives:• Find the domains of rational functions.• Use arrow notation.• Identify vertical asymptotes.• Identify horizontal asymptotes.• Use transformations to graph rational functions.• Graph rational functions.• Identify slant asymptotes.• Solve applied problems involving rational functions.

Page 2: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Rational Functions

Page 3: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Page 4: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Vertical Asymptotes

Page 5: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Page 6: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Page 7: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Horizontal Asymptote

Page 8: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Page 9: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Page 10: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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Slant Asymptote

Page 11: Rational Functions and their graphs€¦ · rational function: 2. f(x) = If n = m, the liney = —L ra h off. is the horizontal asymptote of the Let f be the rational function given

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2.3 Polynomial and Rational Functions Identify a Polynomial Function Identify a Rational Function Find Vertical and Horizontal Asymptotes for Rational.

2.3 Polynomial and Rational Functions Identify a Polynomial Function Identify a Rational Function Find Vertical and Horizontal Asymptotes for Rational.

A rational function f x ratio Elementary Functions ...

A rational function f x ratio Elementary Functions ...

Section 5.3 – The Graph of a Rational Function

Section 5.3 – The Graph of a Rational Function

Henry Speaks for Himself by John Liney - preview

Henry Speaks for Himself by John Liney - preview

Section 4.3 the graph of a rational function

Section 4.3 the graph of a rational function

83 Rational Functions and Their Graphsimages.pcmac.org/SiSFiles/Schools/AL/MadisonCity... · rational function : a function that you can write in the form 83 Rational Functions and

83 Rational Functions and Their Graphsimages.pcmac.org/SiSFiles/Schools/AL/MadisonCity... · rational function : a function that you can write in the form 83 Rational Functions and

Rational Function

Rational Function

Definition of a Rational Function A rational function is a quotient of polynomials that has the form The domain of a rational function consists of all.

Definition of a Rational Function A rational function is a quotient of polynomials that has the form The domain of a rational function consists of all.

Graphing Linear Rational Functions A rational function is a function whose rule is the quotient of two polynomials.

Graphing Linear Rational Functions A rational function is a function whose rule is the quotient of two polynomials.

3.6 Rational Functions & Their Graphs...2014/11/03  · 3.6-Rational Functions & Their Graphs What is a Rational Function? A rational function is a function that is the ratio of two

3.6 Rational Functions & Their Graphs...2014/11/03  · 3.6-Rational Functions & Their Graphs What is a Rational Function? A rational function is a function that is the ratio of two

Rational Functions. To sketch the graph of a rational function: Determine if the function points of discontinuity for the.

Rational Functions. To sketch the graph of a rational function: Determine if the function points of discontinuity for the.

Informal Definition of a Rational Function · 2.6 Rational Functions Informal Definition of a Rational Function – A rational function is a quotient of polynomial functions. It can

Informal Definition of a Rational Function · 2.6 Rational Functions Informal Definition of a Rational Function – A rational function is a quotient of polynomial functions. It can

Section 5.2 – Properties of Rational Functions Defn: Rational Function The functions p and q are polynomials. The domain of a rational function is the.

Section 5.2 – Properties of Rational Functions Defn: Rational Function The functions p and q are polynomials. The domain of a rational function is the.

Rational Function Interpolation Barycentric Rational ...dmitra/SciComp/13Spr/... · Why Rational Function Interpolation? Express more diverse behavior than polynomials Solves disadvantages

Rational Function Interpolation Barycentric Rational ...dmitra/SciComp/13Spr/... · Why Rational Function Interpolation? Express more diverse behavior than polynomials Solves disadvantages

Consider the rational function below.

Consider the rational function below.

A rational model of function learning - cocosci.berkeley.educocosci.berkeley.edu/papers/RationalModelFunctionLearning.pdf · A rational model of function learning ... Abstract Theories

A rational model of function learning - cocosci.berkeley.educocosci.berkeley.edu/papers/RationalModelFunctionLearning.pdf · A rational model of function learning ... Abstract Theories

3.7 Rational Functions - YorkU Math and Statsraguimov/math1510_y13/PreCalc6_03_07... · 2013-12-04 · 3 Rational Functions A rational function is a function of the form where P and

3.7 Rational Functions - YorkU Math and Statsraguimov/math1510_y13/PreCalc6_03_07... · 2013-12-04 · 3 Rational Functions A rational function is a function of the form where P and

Rational Functions Introduction to Rational Functions Function Evaluator and Grapher.

Rational Functions Introduction to Rational Functions Function Evaluator and Grapher.

Rational Function Fitting of Electromagnetic Transfer ... · domain response data, provides for accurate and broadband rational function fitting of the DUT. The resulting rational

Rational Function Fitting of Electromagnetic Transfer ... · domain response data, provides for accurate and broadband rational function fitting of the DUT. The resulting rational

Rational Functions Find the Domain of a function Determine the vertical asymptotes of a rational function Determine the horizontal asymptotes of a rational.

Rational Functions Find the Domain of a function Determine the vertical asymptotes of a rational function Determine the horizontal asymptotes of a rational.