Pre-calculus Books

Book SynopsisIncludes: Print Student EditionTable of ContentsChapter 0 Preparing for Precalculus0-1 Sets0-2 Operations with Complex Numbers0-3 Quadratic Functions and Equations0-4 nth Roots and Real Exponents0-5 Systems of Linear Equations and Inequalities0-6 Matrix Operations0-7 Probability with Permutations and Combinations0-8 StatisticsChapter 1 Functions from a Calculus Perspective1-1 Functions1-2 Analyzing Graphs of Function and Relations1-3 Continuity, End Behavior, and Limits1-4 Extrema and Average Rates of Change1-5 Parent Functions and TransformationsExtend 1-5 Graphing Technology Lab: Nonlinear Inequalities1-6 Function Operations and Composition of Functions1-7 Inverse Relations and FunctionsExtend 1-7 Graphing Technology Lab: Graphing Inverses Using Parametric EquationsChapter 2 Power, Polynomials, and Rational Functions2-1 Power and Radical FunctionsExplore 2-2 Graphing Technology Lab: Behavior and Graphs2-2 Polynomial FunctionsExtend 2-2 Graphing Technology Lab: Hidden Behavior in Graphs2-3 The Remainder and Factor Theorems2-4 Zeros of Polynomial Functions2-5 Rational Functions2-6 Nonlinear InequalitiesChapter 3 Exponential and Logarithmic Functions3-1 Exponential FunctionsExtend 3-1 Graphing Technology Lab: Financial Literacy: Exponential Functions3-2 Logarithmic Functions3-3 Properties of Logarithms3-4 Exponential and Logarithmic EquationsExtend 3-4 Graphing Technology Lab: Exponential and Logarithmic Inequalities3-5 Modeling with Nonlinear RegressionChapter 4 Trigonometric Functions4-1 Right Triangle Trigonometry4-2 Degrees and Radians4-3 Trigonometric Functions on the Unit CircleExplore 4-4 Graphing Technology Lab: Graphing the Sine Function Parametrically4-4 Graphing Sine and Cosine FunctionsExtend 4-4 Graphing Technology Lab: Sums and Differences of Sinusoids4-5 Graphing Other Trigonometric Functions4-6 Inverse Trigonometric Functions4-7 The Law of Sines and the Law of CosinesChapter 5 Trigonometric Identities and Equations5-1 Trigonometric Identities5-2 Verifying Trigonometric Identities5-3 Solving Trigonometric EquationsExtend 5-3 Graphing Technology Lab: Solving Trigonometric Inequalities5-4 Sum and Difference IdentitiesExtend 5-4 Graphing Technology Lab: Reduction Identities5-5 Multiple-Angle and Product-to-Sum IdentitiesChapter 6 Systems of Equations and Matrices6-1 Multivariable Linear Systems and row Operations6-2 Matrix Multiplication, Inverses, and DeterminantsExtend 6-2 Graphing Technology Lab: Determinants and Areas of Polygons6-3 Solving Linear Systems Using Inverses and Cramer’s RuleExtend 6-3 Graphing Technology Lab: Matrices and Cryptography6-4 Partial Fractions6-5 Linear OptimizationChapter 7 Conic Sections and Parametric Equations7-1 Parabolas7-2 Ellipses and Circles7-3 Hyperbolas7-4 Rotations of Conic SectionsExtend 7-4 Graphing Technology Lab: Systems of Nonlinear Equations and Inequalities7-5 Parametric EquationsExtend 7-5 Graphing Technology Lab: Modeling with Parametric EquationsChapter 8 Vectors8-1 Introduction to Vectors8-2 Vectors in the Coordinate Plane8-3 Dot Products and Vector Projections8-4 Vectors in Three-Dimensional SpaceExtend 8-4 Graphing Technology Lab: Vector Transformations with Matrices8-5 Dot and Cross Products of Vectors in SpaceChapter 9 Polar Coordinates and Complex Numbers9-1 Polar CoordinatesExtend 9-1 Graphing Technology Lab: Investigate Graphs of Polar Equations9-2 Graphs of Polar Equations9-3 Polar and Rectangular Forms of Equations9-4 Polar Forms of Conic Sections9-5 Complex Numbers and De Moivre’s TheoremChapter 10 Sequences and Series10-1 Sequences, Series, and Sigma Notation10-2 Arithmetic Sequences and Series10-3 Geometric Sequences and SeriesExtend 10-3 Graphing Technology Lab: Continues Fractions10-4 Mathematical Induction10-5 The Binomial Theorem10-6 Functions as infinite SeriesExtend 10-6 Spreadsheet Lab: Detecting Patterns in DataChapter 11 Inferential Statistics11-1 Descriptive Statistics11-2 Probability Distributions11-3 The Normal DistributionExtend 11-3 Graphing Technology Lab: Transforming Skewed Data11-4 The Central Limit Theorem11-5 Confidence Intervals11-6 Hypothesis Testing11-7 Correlations and Linear RegressionExtend 11-7 Graphing Technology Lab: Median-Fit LinesChapter 12 Limits and Derivatives12-1 Estimating Limits Graphically12-2 Evaluating Limits AlgebraicallyExplore12-3 Graphing Technology Lab: The Slope of a Curve12-3 Tangent Lines and Velocity12-4 Derivatives12-5 Area Under a Curve and Integration12-6 The fundamental Theorem of Calculus

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Book SynopsisIncludes Print Student Edition

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Book SynopsisBob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob's love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to College Algebra, Bob has written textbooks covering developmental mathematics, introductory algebra, intermediate algebra, trigonometry, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson. When not secluded in his Northern California writer's cabin, Bob can be found hTable of ContentsP. Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation P.3 Radicals and Rational Exponents P.4 Polynomials P.5 Factoring Polynomials P.6 Rational Expressions P.7 Equations P.8 Modeling with Equations P.9 Linear Inequalities and Absolute Value Inequalities Summary, Review, and Test Review Exercises Chapter P Test 1. Functions and Graphs 1.1 Graphs and Graphing Utilities 1.2 Basics of Functions and Their Graphs 1.3 More on Functions and Their Graphs 1.4 Linear Functions and Slope 1.5 More on Slope 1.6 Transformations of Functions 1.7 Combinations of Functions; Composite Functions 1.8 Inverse Functions 1.9 Distance and Midpoint Formulas; Circles 1.10 Modeling with Functions 2. Polynomial and Rational Functions 2.1 Complex Numbers 2.2 Quadratic Functions 2.3 Polynomial Functions and Their Graphs 2.4 Dividing Polynomials; Remainder and Factor Theorems 2.5 Zeros of Polynomial Functions 2.6 Rational Functions and Their Graphs 2.7 Polynomial and Rational Inequalities 2.8 Modeling Using Variation 3. Exponential and Logarithmic Functions 3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Properties of Logarithms 3.4 Exponential and Logarithmic Equations 3.5 Exponential Growth and Decay; Modeling Data 4. Trigonometric Functions 4.1 Angles and Radian Measure 4.2 Trigonometric Functions: The Unit Circle 4.3 Right Triangle Trigonometry 4.4 Trigonometric Functions of Any Angle 4.5 Graphs of Sine and Cosine Functions 4.6 Graphs of Other Trigonometric Functions 4.7 Inverse Trigonometric Functions 4.8 Applications of Trigonometric Functions 5. Analytic Trigonometry 5.1 Verifying Trigonometric Identities 5.2 Sum and Difference Formulas 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 5.4 Product-to-Sum and Sum-to-Product Formulas 5.5 Trigonometric Equations 6. Additional Topics in Trigonometry 6.1 The Law of Sines 6.2 The Law of Cosines 6.3 Polar Coordinates 6.4 Graphs of Polar Equations 6.5 Complex Numbers in Polar Form; DeMoivre's Theorem 6.6 Vectors 6.7 The Dot Product 7. Systems of Equations and Inequalities 7.1 Systems of Linear Equations in Two Variables 7.2 Systems of Linear Equations in Three Variables 7.3 Partial Fractions 7.4 Systems of Nonlinear Equations in Two Variables 7.5 Systems of Inequalities 7.6 Linear Programming 8. Matrices and Determinants 8.1 Matrix Solutions to Linear Systems 8.2 Inconsistent and Dependent Systems and Their Applications 8.3 Matrix Operations and Their Applications 8.4 Multiplicative Inverses of Matrices and Matrix Equations 8.5 Determinants and Cramer's Rule 9. Conic Sections and Analytic Geometry 9.1 The Ellipse 9.2 The Hyperbola 9.3 The Parabola 9.4 Rotation of Axes 9.5 Parametric Equations 9.6 Conic Sections in Polar Coordinates 10. Sequences, Induction, and Probability 10.1 Sequences and Summation Notation 10.2 Arithmetic Sequences 10.3 Geometric Sequences and Series 10.4 Mathematical Induction 10.5 The Binomial Theorem 10.6 Counting Principles, Permutations, and Combinations 10.7 Probability 11. Introduction to Calculus 11.1 Finding Limits Using Tables and Graphs 11.2 Finding Limits Using Properties of Limits 11.3 Limits and Continuity 11.4 Introduction to Derivatives

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Book SynopsisTable of ContentsANNOTATED TABLE OF CONTENTS To the instructor: As you know from your experience teaching both Intermediate Algebra and College Algebra courses, there is a great deal of repetition of topics in the two courses. In fact, over 60% of the topics covered in a College Algebra textbook are also covered in an Intermediate Algebra text. This book is intended to eliminate this repetition and consequently to create a course that makes better use of students’ time and resources. Chapter R Review of Basic Algebra Part 1 Operations R.1 The Set of Real Numbers R.2 Operations with Real Numbers R.3 Exponential Notation and Order of Operations Part 2 Manipulations R.4 Introduction to Algebraic Expressions R.5 Equivalent Algebraic Expressions R.6 Simplifying Algebraic Expressions R.7 Properties of Exponents and Scientific Notation 1 Solving Linear Equations and Inequalities The topics in this chapter are often taught in Intermediate Algebra and then again in College Algebra. Here, the repetition is eliminated. 1.1 Solving Equations 1.2 Formulas and Applications 1.3 Applications and Problem Solving 1.4 Sets, Inequalities, and Interval Notation 1.5 Intersections, Unions, and Compound Inequalities 1.6 Absolute-Value Equations and Inequalities 2 Graphs, Functions, and Applications We believe that functions and graphing should be introduced early and continue as a thread that runs through the course. This allows the instructor the opportunity to use the visual element of graphing to show students how solutions of equations, zeros of functions, and x-intercepts of graphs are related. This chapter blends function topics from Intermediate Algebra and College Algebra. 2.1 Graphs of Equations 2.2 Functions and Graphs 2.3 Finding Domain and Range 2.4 The Algebra of Functions 2.5 Linear Functions: Graphs and Slope 2.6 More on Graphing Linear Equations 2.7 Finding Equations of Lines; Applications 3 Systems of Equations This chapter covers systems of equations, a topic that is often taught in both Intermediate Algebra and College Algebra. This is another instance in which repetition of topics is eliminated. In addition, it includes linear programming, a topic that is traditionally in College Algebra but not in Intermediate Algebra. 3.1 Systems of Equations in Two Variables 3.2 Solving by Substitution 3.3 Solving by Elimination 3.4 Solving Applied Problems: Two Equations 3.5 Systems of Equations in Three Variables 3.6 Solving Applied Problems: Three Equations 3.7 Systems of Inequalities and Linear Programming 4 Polynomials and Polynomial Functions This chapter provides thorough coverage of polynomials and polynomial functions, thus laying a solid foundation for the more advanced College Algebra coverage of these topics in Chapter 8. 4.1 Introduction to Polynomials and Polynomial Functions 4.2 Multiplication of Polynomials 4.3 Introduction to Factoring 4.4 Factoring Trinomials: x2 + bx + c 4.5 Factoring Trinomials: ax2 + bx + c, a _1 4.6 Special Factoring 4.7 Factoring: A General Strategy 4.8 Applications of Polynomial Equations and Functions 5 Rational Expressions, Equations, and Functions In this chapter, the student gets a solid basic coverage of rational expressions, rational equations, and rational functions as well as coverage of the difference quotient from College Algebra. This paves the way for studying more advanced College Algebra coverage of many of these topics in Chapter 8. 5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying 5.2 LCMs, LCDs, Addition, and Subtraction 5.3 Division of Polynomials 5.4 Complex Rational Expressions 5.5 Solving Rational Equations 5.6 Applications and Proportions 5.7 Formulas and Applications 5.8 Variation and Applications 6 Radical Expressions, Equations, and Functions This chapter covers traditional Intermediate Algebra topics. In addition, now that the student has studied linear functions, polynomial functions of degree two and higher, rational functions, and radical functions, we have included the College Algebra topics of increasing functions, decreasing functions, and piecewise-defined functions. We weave together topics that are covered early in College Algebra and topics from Intermediate Algebra. (Note that complex numbers are covered in Chapter 7 along with quadratic equations rather than in this chapter.) 6.1 Radical Expressions and Functions 6.2 Rational Numbers as Exponents 6.3 Simplifying Radical Expressions 6.4 Addition, Subtraction, and More Multiplication 6.5 More on Division of Radical Expressions 6.6 Solving Radical Equations 6.7 Applications Involving Powers and Roots 6.8 Increasing, Decreasing, and Piecewise Functions; Applications 7 Quadratic Functions and Equations This chapter blends traditional Intermediate Algebra coverage of quadratic equations with additional, more advanced topics that are traditionally associated with a College Algebra course. 7.1 Symmetry 7.2 Transformations 7.3 The Complex Numbers 7.4 Quadratic Equations, Functions, Zeros, and Models 7.5 Analyzing Graphs of Quadratic Functions 8 Polynomial Functions and Rational Functions Here, College Algebra topics regarding polynomial functions and rational functions are built on the solid foundation that was laid in Chapters 4 and 5. 8.1 Polynomial Functions and Models 8.2 Graphing Polynomials Functions 8.3 Polynomial Division; The Remainder Theorem and the Factor Theorem 8.4 Theorems about Zeros of Polynomial Functions 8.5 Rational Functions 8.6 Polynomial Inequalities and Rational Inequalities 9 Exponential Functions and Logarithmic Functions Traditionally, there is little difference in the Intermediate Algebra coverage vs. College Algebra coverage of the topics in this chapter. This is an excellent opportunity to eliminate repetition and thus streamline students’ investment of time and resources. Although inverse functions are often introduced earlier in a College Algebra course, we introduce them here so that they will be fresh in the students’ minds when they are used to show the relationship between exponential functions and logarithmic functions. 9.1 The Composition of Functions 9.2 Inverse Functions 9.3 Exponential Functions and Graphs 9.4 Logarithmic Functions and Graphs 9.5 Properties of Logarithmic Functions 9.6 Solving Exponential Equations and Logarithmic Equations 9.7 Applications and Models: Growth and Decay; Compound Interest 10 Matrices These are the matrix topics that are traditionally taught in a College Algebra course, often along with systems of equations. Here they are presented in a separate chapter so that systems of equations could be covered earlier in the course with the more traditional Intermediate Algebra topics. 10.1 Matrices and Systems of Equations 10.2 Matrix Operations 10.3 Inverses of Matrices 10.4 Determinants and Cramer’s Rule 11 Conic Sections In the topics of conic sections and nonlinear systems of equations we find another area of considerable overlap in Intermediate Algebra and College Algebra. This is another example of how repetition is eliminated. 11.1 The Parabola 11.2 The Circle and the Ellipse 11.3 The Hyperbola 11.4 Nonlinear Systems of Equations and Inequalities 12 Sequences, Series, and Combinatorics These are traditional College Algebra topics. 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series 12.4 Mathematical Induction 12.5 Combinatorics: Permutations 12.6 Combinatorics: Combinations 12.7 The Binomial Theorem 12.8 Probability Appendix This is a College Algebra topic that is often considered to be optional, so we have presented it in an appendix. A.1 Partial Fractions

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Book SynopsisWhen John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded workTable of ContentsTable of Contents Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1–1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3–1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5–1.6) Summary Review Exercises Test Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1–2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4–2.6) Summary Review Exercises Test Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1–3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3–3.4) Summary Review Exercises Test Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1–4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3–4.4) Unifying Polynomial Functions Summary Review Exercises Test Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4–5.5) Unifying Root Functions Summary Review Exercises Test Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions 6.3 Logarithms and Their Properties 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4–6.6) Summary Review Exercises Test Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1–7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer’s Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4–7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7–7.8) Summary Review Exercises Test Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1–8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3–8.4) Summary Review Exercises Test Further Topics in Algebra 9.1 Sequences and Series 9.2 Arithmetic Sequences and Series 9.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 9.1–9.3) 9.4 Counting Theory 9.5 The Binomial Theorem Reviewing Basic Concepts (Sections 9.4–9.5) 9.6 Mathematical Induction 9.7 Probability Reviewing Basic Concepts (Sections 9.6–9.7) Summary Review Exercises Test Review: Basic Algebraic Concepts R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendix: Formulas from Geometry Instructor’s Answers Answers to Selected Exercises* Index *In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.

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Book SynopsisTable of Contents1. Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1 - 1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3 - 1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5 - 1.6) Summary Review Exercises Test 2. Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1 - 2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4 - 2.6) Summary Review Exercises Test 3. Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1 - 3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3 - 3.4) Summary Review Exercises Test 4. Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1 - 4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3 - 4.4) Unifying Polynomial Functions Summary Review Exercises Test 5. Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications Reviewing Basic Concepts (Sections 5.1 - 5.3) 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4 - 5.5) Unifying Root Functions Summary Review Exercises Test 6. Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions Unifying Exponential Functions 6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1 - 6.3) 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4 - 6.6) Summary Exercises on Functions: Domains, Defining Equations, and Composition Summary Review Exercises Test 7. Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1 - 7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer's Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4 - 7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7 - 7.8) Summary Review Exercises Test 8. Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1 - 8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3 - 8.4) Summary Review Exercises Test 9. Trigonometric Functions and Applications 9.1 Angles, Arcs, and Their Measures 9.2 Trigonometric Functions and Fundamental Identities 9.3 Right Triangles and Evaluating Trigonometric Functions 9.4 Applications of Right Triangles 9.5 The Circular Functions 9.6 Graphs of the Sine and Cosine Functions 9.7 Graphs of the Other Circular Functions 9.8 Harmonic Motion Summary Review Exercises Test 10. Trigonometric Identities and Equations 10.1 Trigonometric Identities 10.2 Sum and Difference Identities 10.3 Further Identities 10.4 The Inverse Circular Functions 10.5 Trigonometric Equations and Inequalities (I) 10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric Functions Summary Review Exercises Test 11. Applications of Trigonometry and Vectors 11.1 The Law of Sines 11.2 The Law of Cosines and Area Formulas 11.3 Vectors and Their Applications 11.4 Trigonometric (Polar) Form of Complex Numbers 11.5 Powers and Roots of Complex Numbers 11.6 Polar Equations and Graphs 11.7 More Parametric Equations Summary Review Exercises Test 12. Further Topics in Algebra 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 12.1 - 12.3) 12.4 Counting Theory 12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 12.4 -12.5) 12.6 Mathematical Induction 12.7 Probability Reviewing Basic Concepts (Sections 12.6 - 12.7) Summary Review Exercises Test R. Review: Basic Algebraic Concepts R.1 Review of Sets R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendices A: Geometry Formulas B: Vectors in Space C: Polar Form of Conic Sections D: Rotation of Axes Instructor's Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index

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Book SynopsisWhen John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded workTable of ContentsTable of Contents Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1–1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3–1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5–1.6) Summary Review Exercises Test Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1–2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4–2.6) Summary Review Exercises Test Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1–3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3–3.4) Summary Review Exercises Test Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1–4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3–4.4) Unifying Polynomial Functions Summary Review Exercises Test Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications Reviewing Basic Concepts (Sections 5.1–5.3) 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4–5.5) Unifying Root Functions Summary Review Exercises Test Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions Unifying Exponential Functions 6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1¿–6.3) 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4–6.6) Summary Exercises on Functions: Domains, Defining Equations, and Composition Summary Review Exercises Test Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1–7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer’s Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4–7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7–7.8) Summary Review Exercises Test Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1–8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3–8.4) Summary Review Exercises Test The Unit Circle and the Functions of Trigonometry 9.1 Angles, Arcs, and Their Measures 9.2 The Unit Circle and Its Functions 9.3 Graphs of the Sine and Cosine Functions 9.4 Graphs of the Other Circular Functions 9.5 Functions of Angles and Fundamental Angles 9.6 Evaluating Trigonometric Functions 9.7 Applications of Right Triangles 9.8 Harmonic Motion Summary Review Exercises Test Trigonometric Identities and Equations 10.1 Trigonometric Identities 10.2 Sum and Difference Identities 10.3 Further Identities 10.4 The Inverse Circular Functions 10.5 Trigonometric Equations and Inequalities (I) 10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric Functions Summary Review Exercises Test Applications of Trigonometry and Vectors 11.1 The Law of Sines 11.2 The Law of Cosines and Area Formulas 11.3 Vectors and Their Applications 11.4 Trigonometric (Polar) Form of Complex Numbers 11.5 Powers and Roots of Complex Numbers 11.6 Polar Equations and Graphs 11.7 More Parametric Equations Summary Review Exercises Test Further Topics in Algebra 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 9.1–9.3) 12.4 Counting Theory 12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 9.4–9.5) 12.6 Mathematical Induction 12.7 Probability Reviewing Basic Concepts (Sections 9.6–9.7) Summary Review Exercises Test Limits, Derivatives, and Definite Integrals 13.1 An Introduction to Limits 13.2 Techniques for Calculating Limits 13.3 One-Sided Limits and Limits Involving Infinity 13.4 Tangent Lines and Derivatives 13.5 Area and the Definite Integral Review: Basic Algebraic Concepts R.1 Review of Sets R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendix A: Geometry Formulas Appendix B: Vectors in Space Appendix C: Polar Form of Conic Sections Appendix D: Rotation of Axes Instructor’s Answers Answers to Selected Exercises* Index *In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.

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Book SynopsisJ.S. Ratti has been teaching mathematics at all levels for over 35 years. He is currently a full professor and past chair of mathematics at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has received several awardsincluding a USF Research Council Grant, USF Teaching Incentive Program (TIP) Award, USF Outstanding Undergraduate Teaching Award, and Academy of Applied Sciences grantsand is the coauthor of a successful finite mathematics textbook. He enjoys both college and professional football as well as traveling. Marcus McWaters is currently an Associate Professor at the University of South Florida (USF). He is a former Chair of the Department of Mathematics and Statistics at USF. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. ATable of ContentsTable of Contents BASIC CONCEPTS OF ALGEBRA P.1 The Real Numbers and Their Properties P.2 Integer Exponents and Scientific Notation P.3 Polynomials P.4 Factoring Polynomials P.5 Rational Expressions P.6 Rational Exponents and Radicals Chapter P Review and Tests Review Exercises Practice Test EQUATIONS AND INEQUALITIES 1.1 Linear Equations in One Variable 1.2 Applications of Linear Equations: Modeling 1.3 Quadratic Equations 1.4 Complex Numbers: Quadratic Equations with Complex Solutions 1.5 Solving Other Types of Equations 1.6 Inequalities 1.7 Equations and Inequalities Involving Absolute Value Chapter 1 Review and Tests Review Exercises Practice Test A Practice Test B GRAPHS AND FUNCTIONS 2.1 The Coordinate Plane 2.2 Graphs of Equations 2.3 Lines 2.4 Functions 2.5 Properties of Functions 2.6 A Library of Functions 2.7 Transformations of Functions 2.8 Combining Functions; Composite Functions 2.9 Inverse Functions Chapter 2 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—2 POLYNOMIAL AND RATIONAL FUNCTIONS 3.1 Quadratic Functions 3.2 Polynomial Functions 3.3 Dividing Polynomials 3.4 The Real Zeros of a Polynomial Function 3.5 The Complex Zeros of a Polynomial Function 3.6 Rational Functions 3.7 Variation Chapter 3 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—3 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Rules of Logarithms 4.4 Exponential and Logarithmic Equations and Inequalities 4.5 Logarithmic Scales; Modeling Chapter 4 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—4 TRIGONOMETRIC FUNCTIONS 5.1 Angles and Their Measure 5.2 Right-Triangle Trigonometry 5.3 Trigonometric Functions of Any Angle; The Unit Circle 5.4 Graphs of the Sine and Cosine Functions 5.5 Graphs of the Other Trigonometric Functions 5.6 Inverse Trigonometric Functions Chapter 5 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—5 TRIGONOMETRIC IDENTITIES AND EQUATIONS 6.1 Trigonometric Identities 6.2 Sum and Difference Formulas 6.3 Double-Angle and Half-Angle Formulas 6.4 Product-to-Sum and Sum-to-Product Formulas 6.5 Trigonometric Equations I 6.6 Trigonometric Equations II Chapter 6 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—6 APPLICATIONS OF TRIGONOMETRIC FUNCTIONS 7.1 The Law of Sines 7.2 The Law of Cosines 7.3 Areas of Polygons Using Trigonometry 7.4 Vectors 7.5 The Dot Product 7.6 Polar Coordinates 7.7 Polar Form of Complex Numbers; DeMoivre’s Theorem Chapter 7 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—7 SYSTEMS OF EQUATIONS AND INEQUALITIES 8.1 Systems of Linear Equations in Two Variables 8.2 Systems of Linear Equations in Three Variables 8.3 Partial-Fraction Decomposition 8.4 Systems of Nonlinear Equations 8.5 Systems of Inequalities 8.6 Linear Programming Chapter 8 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—8 MATRICES AND DETERMINANTS 9.1 Matrices and Systems of Equations 9.2 Matrix Algebra 9.3 The Matrix Inverse 9.4 Determinants and Cramer’s Rule Chapter 9 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—9 CONIC SECTIONS 10.1 Conic Sections: Overview 10.2 The Parabola 10.3 The Ellipse 10.4 The Hyperbola Chapter 10 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—10 FURTHER TOPICS IN ALGEBRA 11.1 Sequences and Series 11.2 Arithmetic Sequences; Partial Sums 11.3 Geometric Sequences and Series 11.4 Mathematical Induction 11.5 The Binomial Theorem 11.6 Counting Principles 11.7 Probability Chapter 11 Review and Tests Review Exercises Practice Test A Practice Test B Cumulative Review Exercises Chapters P—11 Answers to Selected Exercises Credits Index

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Book SynopsisNOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of the MyLabTM and MasteringTM platforms exist for each title, and registrations are not transferable. To register for and use MyLab or Mastering, you may also need aCourse ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the MyLab platform may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. For courses in College Algebra. This package includes MyLab Math. Prepare. Practice. Review. Michael Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing<Table of ContentsTable of Contents Review R.1 Real Numbers R.2 Algebra Essentials R.3 Geometry Essentials R.4 Polynomials R.5 Factoring Polynomials R.6 Synthetic Division R.7 Rational Expressions R.8 nth Roots; Rational Exponents Equations and Inequalities 1.1 Linear Equations 1.2 Quadratic Equations 1.3 Complex Numbers; Quadratic Equations in the Complex Number System 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations 1.5 Solving Inequalities 1.6 Equations and Inequalities Involving Absolute Value 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications Chapter 1 Review, Test, and Projects Graphs 2.1 The Distance and Midpoint Formulas 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 2.3 Lines 2.4 Circles 2.5 Variation Chapter 2 Review, Test, and Projects Functions and Their Graphs 3.1 Functions 3.2 The Graph of a Function 3.3 Properties of Functions 3.4 Library of Functions; Piecewise-defined Functions 3.5 Graphing Techniques: Transformations 3.6 Mathematical Models: Building Functions Chapter 3 Review, Test, and Projects Linear and Quadratic Functions 4.1 Properties of Linear Functions and Linear Models 4.2 Building Linear Models from Data 4.3 Quadratic Functions and Their Properties 4.4 Build Quadratic Models from Verbal Descriptions and from Data 4.5 Inequalities Involving Quadratic Functions Chapter 4 Review, Test, and Projects Polynomial and Rational Functions 5.1 Polynomial Functions 5.2 Graphing Polynomials Functions; Models 5.3 Properties of Rational Functions 5.4 The Graph of a Rational Function 5.5 Polynomial and Rational Inequalities 5.6 The Real Zeros of a Polynomial Function Chapter 5 Review, Test, and Projects Exponential and Logarithmic Functions 6.1 Composite Functions 6.2 One-to-One Functions; Inverse Functions 6.3 Exponential Functions 6.4 Logarithmic Functions 6.5 Properties of Logarithms 6.6 Logarithmic and Exponential Equations 6.7 Financial Models 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 6.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter 6 Review, Test, and Projects Analytic Geometry 7.1 Conics 7.2 The Parabola 7.3 The Ellipse 7.4 The Hyperbola Chapter 7 Review, Test, and Projects Systems of Equations and Inequalities 8.1 Systems of Linear Equations: Substitution and Elimination 8.2 Systems of Linear Equations: Matrices 8.3 Systems of Linear Equations: Determinants 8.4 Matrix Algebra 8.5 Partial Fraction Decomposition 8.6 Systems of Nonlinear Equations 8.7 Systems of Inequalities 8.8 Linear Programming Chapter 8 Review, Test, and Projects Sequences; Induction; the Binomial Theorem 9.1 Sequences 9.2 Arithmetic Sequences 9.3 Geometric Sequences; Geometric Series 9.4 Mathematical Induction 9.5 The Binomial Theorem Chapter 9 Review, Test, and Projects Counting and Probability 10.1 Counting 10.2 Permutations and Combinations 10.3 Probability Chapter 10 Review, Test, and Projects Appendix: Graphing Utilities A.1 The Viewing Rectangle A.2 Using a Graphing Utility to Graph Equations A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry A.4 Using a Graphing Utility to Solve Equations A.5 Square Screens A.6 Using a Graphing Utility to Graph Inequalities A.7 Using a Graphing Utility to Solve Systems of Linear Equations Answers Credits Index

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