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| Preface | |
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| Guide to Success | |
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| Basic Concepts of Algebra | |
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| the Real-Number System | |
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| Integer Exponents, Scientific Notation, and Order of Operations | |
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| Addition, Subtraction, and Multiplication of Polynomials | |
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| Factoring | |
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| the Basics of Equation Solving | |
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| Rational Expressions | |
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| Radical Notation and Rational Exponents | |
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| Graphs, Functions, and Models | |
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| Introduction to Graphing | |
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| Functions and Graphs | |
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| Linear Functions, Slope, and Applications | |
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| Equations of Lines and Modeling | |
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| Linear Equations, Functions, Zeros, and Applications | |
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| Solving Linear Inequalities | |
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| More on Functions | |
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| Increasing, Decreasing, and Piecewise Functions; Applications | |
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| the Algebra of Functions | |
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| the Composition of Functions | |
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| Symmetry | |
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| Transformations | |
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| Variation and Applications | |
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| Quadratic Functions and Equations; Inequalities | |
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| the Complex Numbers | |
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| Quadratic Equations, Functions, Zeros, and Models | |
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| Analyzing Graphs of Quadratic Functions | |
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| Solving Rational Equations and Radical Equations | |
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| Solving Equations and Inequalities with Absolute Value | |
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| Polynomial and Rational Functions | |
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| Polynomial Functions and Modeling | |
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| Graphing Polynomial Functions | |
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| Polynomial Division; the Remainder Theorem and the Factor Theorem | |
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| Theorems about Zeros of Polynomial Functions | |
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| Rational Functions | |
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| Polynomial Inequalities and Rational Inequalities | |
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| Exponential and Logarithmic Functions | |
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| Inverse Functions | |
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| Exponential Functions and Graphs | |
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| Logarithmic Functions and Graphs | |
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| Properties of Logarithmic Functions | |
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| Solving Exponential and Logarithmic Equations | |
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| Applications and Models: Growth and Decay; Compound Interest | |
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| the Trigonometric Functions | |
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| Trigonometric Functions of Acute Angles | |
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| Applications of Right Triangles | |
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| Trigonometric Functions of Any Angle | |
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| Radians, Arc Length, and Angular Speed | |
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| Circular Functions: Graphs and Properties | |
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| Graphs of Transformed Sine and Cosine Functions | |
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| Trigonometric Identities, Inverse Functions, and Equations | |
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| Identities: Pythagorean and Sum and Difference | |
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| Identities: Cofunction, Double-Angle, and Half-Angle | |
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| Proving Trigonometric Identities | |
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| Inverses of the Trigonometric Functions | |
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| Solving Trigonometric Equations | |
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| Applications of Trigonometry | |
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| the Law of Sines | |
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| the Law of Cosines | |
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| Complex Numbers: Trigonometric Form | |
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| Polar Coordinates and Graphs | |
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| Vectors and Applications | |
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| Vector Operations | |
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| Systems of Equations and Matrices | |
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| Systems of Equations in Two Variables | |
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| Systems of Equations in Three Variables | |
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| Matrices and Systems of Equations | |
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| Matrix Operations | |
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| Inverses of Matrices | |
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| Determinants and Cramer's Rule | |
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| Systems of Inequalities and Linear Programming | |
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| Partial Fractions | |
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| Analytic Geometry Topics | |
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| the Parabola | |
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| the Circle and the Ellipse | |
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| the Hyperbola | |
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| Nonlinear Systems of Equations and Inequalities | |
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| Rotation of Axes | |
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| Polar Equations of Conics | |
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| Parametric Equations | |
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| Sequences, Series, and Combinatorics | |
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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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| Mathematical Induction | |
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| Combinatorics: Permutations | |
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| Combinatorics: Combinations | |
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| the Binomial Theorem | |
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| Probability | |
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| Photo Credits | |
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| Answers | |
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| Index of Applications | |
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| Index | |