Description
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 work
Table of Contents
Table of Contents
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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
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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
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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
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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
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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
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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.
