Graphical Approach to Precalculus with Limits, A

About our authors When 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 25 years of teaching at the high school and university levels and 15 years of writing mathematics textbooks, all 3 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 works of Frankie Valli and the Four Seasons.The late Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology, and trips to various digs and ruin sites produced fascinating problems for her textbooks, involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate and graduate students, and adult education classes. Now retired, he most recently served as professor of mathematics at Minnesota State University - Mankato. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy and computer science. Outside of mathematics, he enjoys spending time with his lovely wife and 2 children.

• Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1–1.2)1.3 Linear Functions1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3–1.4)1.5 Linear Equations and InequalitiesUnifying Linear Functions1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5–1.6)SummaryReview ExercisesTestAnalysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry2.2 Vertical and Horizontal Shifts of Graphs2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1–2.3)2.4 Absolute Value Functions Unifying Absolute Value Functions2.5 Piecewise-Defined Functions2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4–2.6)SummaryReview ExercisesTestQuadratic Functions 3.1 Complex Numbers3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1–3.2)3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3–3.4)SummaryReview ExercisesTestPolynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions4.2 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 FunctionsSummaryReview ExercisesTestRational, 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 Roots5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4–5.5)Unifying Root FunctionsSummaryReview ExercisesTestInverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions6.2 Exponential Functions Unifying Exponential Functions6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1¿–6.3)6.4 Logarithmic Functions6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions6.6 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 CompositionSummaryReview ExercisesTestSystems and Matrices 7.1 Systems of Equations7.2 Solution of Linear Systems in Three Variables7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1–7.3)7.4 Matrix Properties and Operations7.5 Determinants and Cramer’s Rule7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4–7.6)7.7 Systems of Inequalities and Linear Programming7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7–7.8)SummaryReview ExercisesTestConic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1–8.2)8.3 The Conic Sections and Nonlinear Systems8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3–8.4)SummaryReview ExercisesTestThe Unit Circle and the Functions of Trigonometry 9.1 Angles, Arcs, and Their Measures9.2 The Unit Circle and Its Functions9.3 Graphs of the Sine and Cosine Functions9.4 Graphs of the Other Circular Functions9.5 Functions of Angles and Fundamental Angles9.6 Evaluating Trigonometric Functions9.7 Applications of Right Triangles9.8 Harmonic MotionSummaryReview ExercisesTestTrigonometric Identities and Equations 10.1 Trigonometric Identities10.2 Sum and Difference Identities10.3 Further Identities10.4 The Inverse Circular Functions10.5 Trigonometric Equations and Inequalities (I)10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric FunctionsSummaryReview ExercisesTestApplications of Trigonometry and Vectors 11.1 The Law of Sines11.2 The Law of Cosines and Area Formulas11.3 Vectors and Their Applications11.4 Trigonometric (Polar) Form of Complex Numbers11.5 Powers and Roots of Complex Numbers11.6 Polar Equations and Graphs11.7 More Parametric EquationsSummaryReview ExercisesTestFurther Topics in Algebra 12.1 Sequences and Series12.2 Arithmetic Sequences and Series12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 9.1–9.3)12.4 Counting Theory12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 9.4–9.5)12.6 Mathematical Induction12.7 Probability Reviewing Basic Concepts (Sections 9.6–9.7)SummaryReview ExercisesTestLimits, Derivatives, and Definite Integrals 13.1 An Introduction to Limits13.2 Techniques for Calculating Limits13.3 One-Sided Limits and Limits Involving Infinity13.4 Tangent Lines and Derivatives13.5 Area and the Definite IntegralReview: Basic Algebraic Concepts R.1 Review of SetsR.2 Review of Exponents and PolynomialsR.3 Review of FactoringR.4 Review of Rational ExpressionsR.5 Review of Negative and Rational ExponentsR.6 Review of RadicalsTestAppendices A. Geometry FormulasB. Vectors in SpaceC. Polar Form of Conic SectionsD. Rotation of AxesInstructor’s AnswersAnswers to Selected Exercises*Index *In the AIE, Instructor’s Answers replaces Answers to Selected Exercises.