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Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 3 Polynomial and Rational Functions

3 Polynomial and Rational Functions Chapter Outline 3.1Quadratic Functions and Applications 3.2Synthetic Division; the Remainder and Factor Theorems 3.3The Zeroes of Polynomial Functions 3.4Graphing Polynomial Functions 3.5Graphing Rational Functions 3.6Additional Insights into Rational Functions 3.7Polynomial and Rational Inequalities 3.8Variation: Function Models in Action 1-2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Learning Objectives In Section 3.1 you will learn how to:  A.Graph quadratic functions by completing the square  B.Graph quadratic functions using the vertex formula  C.Find the equation of a quadratic functions from its graph  D.Solve applications involving extreme values 3.1 Quadratic Functions and Applications 1-3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.2 you will learn how to:  A.Divide polynomials using long division and synthetic division  B.Use the remainder theorem to evaluate polynomials  C.Use the factor theorem to factor and build polynomials  D.Solve applications using the remainder theorem 3.2 Synthetic Division; the Remainder and Factor Theorems 1-17 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1-19 EXAMPLE 1 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.3 you will learn how to:  A.Apply the fundamental theorem of algebra and the linear factorization theorem  B.Locate zeroes of polynomials using the intermediate value theorem  C.Find rational zeroes of polynomials using the rational zeroes theorem  D.Use Descartes’ rule of signs and the upper/lower bounds theorem  E.Solve applications of polynomials 3.3 The Zeroes of Polynomial Functions 1-34 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.4 you will learn how to:  A.Identify the graph of a polynomial function and determine its degree  B.Describe the end behavior of a polynomial graph  C.Discuss the attributes of a polynomial graph with zeroes of multiplicity  D.Graph polynomial functions in standard form  E.Solve applications of polynomials 3.4 Graphing Polynomial Functions 1-63 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.5 you will learn how to:  A.Identify horizontal and vertical asymptotes  B.Find the domain of a rational function  C.Apply the concept of “multiplicity” to rational graphs  D.Find the horizontal asymptotes of a rational function  E.Graph rational functions  F.Solve applications of rational functions 3.5 Graphing Rational Functions 1-88 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.6 you will learn how to:  A.Graph rational functions with removable discontinuities  B.Graph rational functions with oblique or nonlinear asymptotes  C.Solve applications involving rational functions 3.6 Additional Insights into Rational Functions Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.7 you will learn how to:  A.Solve quadratic inequalities  B.Solve polynomial inequalities  C.Solve rational inequalities  D.Use interval tests to solve inequalities  E.Solve applications of inequalities 3.7 Polynomial and Rational Inequalities Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Learning Objectives In Section 3.8 you will learn how to:  A.Solve direct variations  B.Solve inverse variations  C.Solve joint variations 3.8 Variation: Function Models in Action Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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