Graphical Approach to Precalculus with Limits

John Hornsby: 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 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 works of Frankie Valli and the Four Seasons.  Marge Lial (late) 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 two children.

• 1. Linear Functions, Equations, and Inequalities1.1 Real Numbers and the Rectangular Coordinate System1.2 Introduction to Relations and Functions1.3 Linear Functions1.4 Equations of Lines and Linear Models1.5 Linear Equations and Inequalities1.6 Applications of Linear Functions  2. Analysis of Graphs of Functions2.1 Graphs of Basic Functions and Relations; Symmetry2.2 Vertical and Horizontal Shifts of Graphs2.3 Stretching, Shrinking, and Reflecting Graphs2.4 Absolute Value Functions2.5 Piecewise-Defined Functions2.6 Operations and Composition  3. Polynomial Functions3.1 Complex Numbers3.2 Quadratic Functions and Graphs3.3 Quadratic Equations and Inequalities3.4 Applications of Quadratic Functions and Models3.5 Higher-Degree Polynomial Functions and Graphs3.6 Topics in the Theory of Polynomial Functions (I)3.7 Topics in the Theory of Polynomial Functions (II)3.8 Polynomial Equations and Inequalities; Further Applications and Models  4. Rational, Power, and Root Functions4.1 Rational Functions and Graphs I4.2 Rational Functions and Graphs II4.3 Rational Equations, Inequalities, Models, and Applications4.4 Functions Defined by Powers and Roots4.5 Equations, Inequalities, and Applications Involving Root Functions  5. Inverse, Exponential, and Logarithmic Functions5.1 Inverse Functions5.2 Exponential Functions5.3 Logarithms and Their Properties5.4 Logarithmic Functions5.5 Exponential and Logarithmic Equations and Inequalities5.6 Further Applications and Modeling with Exponential and Logarithmic Functions  6. Systems and Matrices6.1 Systems of Equations6.2 Solution of Linear Systems in Three Variables6.3 Solution of Linear Systems by Row Transformations6.4 Matrix Properties and Operations6.5 Determinants and Cramer’s Rule6.6 Solution of Linear Systems by Matrix Inverses6.7 Systems of Inequalities and Linear Programming6.8 Partial Fractions  7. Analytic Geometry and Nonlinear Systems7.1 Circles and Parabolas7.2 Ellipses and Hyperbolas7.3 The Conic Sections and Nonlinear Systems7.4 Parametric Equations  8. The Unit Circle and Functions of Trigonometry8.1 Angles, Arcs, and Their Measures8.2 The Unit Circle and Its Functions8.3 Graphs of the Sine and Cosine Functions8.4 Graphs of the Other Circular Functions8.5 Functions of Angles and Fundamental Angles8.6 Evaluating Trigonometric Functions8.7 Applications of Right Triangles8.8 Harmonic Motion  9. Trigonometric Identities and Equations9.1 Trigonometric Identities9.2 Sum and Difference Identities9.3 Further Identities9.4 The Inverse Circular Functions9.5 Trigonometric Equations and Inequalities (I)9.6 Trigonometric Equations and Inequalities (II)  10. Applications of Trigonometry and Vectors10.1 The Law of Sines10.2 The Law of Cosines and Area Formulas10.3 Vectors and Their Applications10.4 Trigonometric (Polar) Form of Complex Numbers10.5 Powers and Roots of Complex Numbers10.6 Polar Equations and Graphs10.7 More Parametric Equations  11. Further Topics in Algebra11.1 Sequences and Series11.2 Arithmetic Sequences and Series11.3 Geometric Sequences and Series11.4 Counting Theory11.5 The Binomial Theorem11.6 Mathematical Induction11.7 Probability  12. Limits, Derivatives, and Definite Integrals12.1 An Introduction to Limits12.2 Techniques for Calculating Limits12.3 One-Sided Limits and Limits Involving Infinity12.4 Tangent Lines and Derivatives12.5 Area and the Definite Integral  R. Reference: Basic Algebraic ConceptsR.1 Review of Exponents and PolynomialsR.2 Review of FactoringR.3 Review of Rational ExpressionsR.4 Review of Negative and Rational ExponentsR.5 Review of Radicals