Graphical Approach to Algebra & Trigonometry, 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.

• 1. Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System1.2 Introduction to Relations and FunctionsReviewing Basic Concepts (Sections 1.1 - 1.2)1.3 Linear Functions1.4 Equations of Lines and Linear ModelsReviewing Basic Concepts (Sections 1.3 - 1.4)1.5 Linear Equations and InequalitiesUnifying Linear Functions1.6 Applications of Linear FunctionsReviewing Basic Concepts (Sections 1.5 - 1.6)SummaryReview ExercisesTest2. Analysis 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 GraphsReviewing Basic Concepts (Sections 2.1 - 2.3)2.4 Absolute Value FunctionsUnifying Absolute Value Functions2.5 Piecewise-Defined Functions2.6 Operations and CompositionReviewing Basic Concepts (Sections 2.4 - 2.6)SummaryReview ExercisesTest3. Quadratic Functions 3.1 Complex Numbers3.2 Quadratic Functions and GraphsReviewing Basic Concepts (Sections 3.1 - 3.2)3.3 Quadratic Equations and InequalitiesUnifying Quadratic Functions3.4 Applications of Quadratic Functions and ModelsReviewing Basic Concepts (Sections 3.3 - 3.4)SummaryReview ExercisesTest4. Polynomial 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 ModelsReviewing Basic Concepts (Sections 4.3 - 4.4)Unifying Polynomial FunctionsSummaryReview ExercisesTest5. 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 ApplicationsReviewing Basic Concepts (Sections 5.1 - 5.3)5.4 Functions Defined by Powers and Roots5.5 Equations, Inequalities, and Applications Involving Root FunctionsReviewing Basic Concepts (Sections 5.4 - 5.5)Unifying Root FunctionsSummaryReview ExercisesTest6. Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions6.2 Exponential FunctionsUnifying Exponential Functions6.3 Logarithms and Their PropertiesReviewing Basic Concepts (Sections 6.1 - 6.3)6.4 Logarithmic Functions6.5 Exponential and Logarithmic Equations and InequalitiesUnifying Logarithmic Functions6.6 Further Applications and Modeling with Exponential and Logarithmic FunctionsReviewing Basic Concepts (Sections 6.4 - 6.6)Summary Exercises on Functions: Domains, Defining Equations, and CompositionSummaryReview ExercisesTest7. Systems and Matrices 7.1 Systems of Equations7.2 Solution of Linear Systems in Three Variables7.3 Solution of Linear Systems by Row TransformationsReviewing 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 InversesReviewing Basic Concepts (Sections 7.4 - 7.6)7.7 Systems of Inequalities and Linear Programming7.8 Partial FractionsReviewing Basic Concepts (Sections 7.7 - 7.8)SummaryReview ExercisesTest8. Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas8.2 Ellipses and HyperbolasReviewing Basic Concepts (Sections 8.1 - 8.2)8.3 The Conic Sections and Nonlinear Systems8.4 Introduction to Parametric EquationsReviewing Basic Concepts (Sections 8.3 - 8.4)SummaryReview ExercisesTest9. Trigonometric Functions and Applications 9.1 Angles, Arcs, and Their Measures9.2 Trigonometric Functions and Fundamental Identities9.3 Right Triangles and Evaluating Trigonometric Functions9.4 Applications of Right Triangles9.5 The Circular Functions9.6 Graphs of the Sine and Cosine Functions9.7 Graphs of the Other Circular Functions9.8 Harmonic MotionSummaryReview ExercisesTest10. Trigonometric 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 ExercisesTest11. Applications 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 ExercisesTest12. Further Topics in Algebra 12.1 Sequences and Series12.2 Arithmetic Sequences and Series12.3 Geometric Sequences and SeriesReviewing Basic Concepts (Sections 12.1 - 12.3)12.4 Counting Theory12.5 The Binomial TheoremReviewing Basic Concepts (Sections 12.4 -12.5)12.6 Mathematical Induction12.7 ProbabilityReviewing Basic Concepts (Sections 12.6 - 12.7)SummaryReview ExercisesTestR. Review: 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 Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index