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Linear Functions, Equations, and Inequalities | |
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Real Numbers and the Rectangular Coordinate System | |
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Introduction to Relations and Functions | |
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Reviewing Basic Concepts | |
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Linear Functions | |
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Equations of Lines and Linear Models | |
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Reviewing Basic Concepts | |
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Linear Equations and Inequalities | |
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Applications of Linear Functions | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Analysis of Graphs of Functions | |
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Graphs of Basic Functions and Relations; Symmetry | |
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Vertical and Horizontal Shifts of Graphs | |
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Stretching, Shrinking, and Reflecting Graphs | |
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Reviewing Basic Concepts | |
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Absolute Value Functions | |
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Piecewise-Defined Functions | |
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Operations and Composition | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Polynomial Functions | |
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Complex Numbers | |
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Quadratic Functions and Graphs | |
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Quadratic Equations and Inequalities | |
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Reviewing Basic Concepts | |
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Further Applications of Quadratic Functions and Models | |
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Higher-Degree Polynomial Functions and Graphs | |
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Reviewing Basic Concepts | |
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Topics in the Theory of Polynomial Functions I | |
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Topics in the Theory of Polynomial Functions II 3.8 Polynomial Equations and Inequalities; Further Applications and Models | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Rational, Power, and Root Functions | |
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Rational Functions and Graphs | |
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More on Rational Functions and Graphs | |
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Rational Equations, Inequalities, Models, and Applications | |
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Reviewing Basic Concepts | |
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Functions Defined by Powers and Roots | |
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Equations, Inequalities, and Applications Involving Root Functions | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Inverse, Exponential, and Logarithmic Functions | |
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Inverse Functions | |
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Exponential Functions | |
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Logarithms and Their Properties | |
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Reviewing Basic Concepts | |
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Logarithmic Functions | |
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Exponential and Logarithmic Equations and Inequalities | |
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Reviewing Basic Concepts | |
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Further Applications and Modeling with Exponential and Logarithmic Functions | |
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Summary | |
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Review Exercises | |
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Test | |
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Analytic Geometry | |
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Circles and Parabolas | |
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Ellipses and Hyperbolas | |
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Reviewing Basic Concepts | |
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Summary of Conic Sections | |
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Parametric Equations | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Systems of Equations and Inequalities; Matrices | |
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Systems of Equations | |
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Solution of Linear Systems in Three Variables | |
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Solution of Linear Systems by Row Transformations | |
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Reviewing Basic Concepts | |
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Matrix Properties and Operations | |
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Determinants and Cramer's Rule | |
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Solution of Linear Systems by Matrix Inverses | |
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Reviewing Basic Concepts | |
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Systems of Inequalities and Linear Programming | |
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Partial Fractions | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Trigonometric Functions and Their Applications | |
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Angles and Their Measures | |
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Trigonometric Functions and Fundamental Identities | |
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Reviewing Basic Concepts | |
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Evaluating Trigonometric Functions | |
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Applicationis of Right Triangles | |
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Reviewing Basic Concepts | |
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The Circular Functions | |
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Graphs of the Sine and Cosine Functions | |
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Graphs of the Other Circular Functions | |
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Harmonic Motion | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Trigonometric Identities and Equations | |
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Trigonometric Identities | |
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Sum and Difference Identities | |
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Reviewing Basic Concepts | |
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Further Identities | |
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The Inverse Circular Functions | |
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Reviewing Basic Concepts | |
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Trigonometric Equations and Inequalities (I) | |
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Trigonometric Equations and Inequalities (II) | |
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Summary | |
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Review Exercises | |
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Test | |
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Applications of Trigonometry and Vectors | |
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The Law of Sines | |
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The Law of Cosines and Area Formulas | |
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Vectors and Their Applications | |
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Reviewing Basic Concepts | |
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Trigonometric (Polar) Form of Complex Numbers | |
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Powers and Roots of Complex Numbers | |
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Reviewing Basic Concepts | |
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Polar Equations and Graphs | |
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More Parametric Equations | |
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Reviewing Basic Concepts | |
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Summary | |
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Review Exercises | |
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Test | |
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Further Topics in Algebra | |
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Sequences and Series | |
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Arithmetic Sequences and Series | |
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Geometric Sequences and Series | |
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The Binomial Theorem | |
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Mathematical Induction | |
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Counting Theory | |
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Probability | |
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Review Exercises | |
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Test | |
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Chapter R Reference: Basic Algebraic Concepts | |
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Review of Exponents and Polynomials | |
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Review of Factoring | |
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Review of Rational Expressions | |
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Review of Negative and Rational Exponents | |
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Review of Radicals | |
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Chapter R Test | |
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Summary | |
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Review Exercises | |
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Test | |
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Appendix Geometry Formulas | |
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Answers to Selected Exercises | |
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Index | |