# Alignment: Precalculus • Sullivan • Tenth Edition

• 1 Graphs
• 1.1 The Distance and Midpoint Formulas
• 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
• 1.3 Lines
• 1.4 Circles
• 2 Functions and Their Graphs
• 2.1 Functions
• 2.2 The Graph of a Function
• 2.3 Properties of Functions
• 2.4 Library of Functions: Piecewise-Defined Functions
• 2.5 Graphing Techniques: Transformations
• 2.6 Mathematical Models: Building Functions
• 3 Linear and Quadratic Functions
• 3.1 Properties of Linear Functions and Linear Models
• 3.2 Building Linear Models from Data
• 3.3 Quadratic Functions and Their Properties
• 3.4 Build Quadratic Models from Verbal Descriptions and from Data
• 3.5 Inequalities Involving Quadratic Functions
• 4 Polynomial and Rational Functions
• 4.1 Polynomial Functions and Models
• 4.2 Properties of Rational Functions
• 4.3 The Graph of a Rational Function
• 4.4 Polynomial and Rational Inequalities
• 4.5 The Real Zeros of a Polynomial Function
• 4.6 Complex Zeros: Fundamental Theorem of Algebra
• 5 Exponential and Logarithmic Functions
• 5.1 Composite Functions
• 5.2 One-to-One Functions; Inverse Functions
• 5.3 Exponential Functions
• 5.4 Logarithmic Functions
• 5.5 Properties of Logarithms
• 5.6 Logarithmic and Exponential Equations
• 5.7 Financial Models
• 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
• 5.9 Building Exponential, Logarithmic, and Logistic Models from Data
• 6 Trigonometric Functions
• 6.1 Angles and Their Measure
• 6.2 Trigonometric Functions: Unit Circle Approach
• 6.3 Properties of the Trigonometric Functions
• 6.4 Graphs of the Sine and Cosine Functions
• 6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
• 6.6 Phase Shift; Sinusoidal Curve Fitting
• 7 Analytic Trigonometry
• 7.1 The Inverse Sine, Cosine, and Tangent Functions
• 7.2 The Inverse Trigonometric Functions (Continued)
• 7.3 Trigonometric Equations
• 7.4 Trigonometric Identities
• 7.5 Sum and Difference Formulas
• 7.6 Double-Angle and Half-Angle Formulas
• 7.7 Product-to-Sum and Sum-to-Product Formulas
• 8 Applications of Trigonometric Functions
• 8.1 Right Triangle Trigonometry; Applications
• 8.2 The Law of Sines
• 8.3 The Law of Cosines
• 8.4 Area of a Triangle
• 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
• 9 Polar Coordinates; Vectors
• 9.1 Polar Coordinates
• 9.2 Polar Equations and Graphs
• 9.3 The Complex Plane; De Moivre’s Theorem
• 9.4 Vectors
• 9.5 The Dot Product
• 9.6 Vectors in Space
• 9.7 The Cross Product
• 10 Analytic Geometry
• 10.1 Conics
• 10.2 The Parabola
• 10.3 The Ellipse
• 10.4 The Hyperbola
• 10.5 Rotation of Axes; General Form of a Conic
• 10.6 Polar Equations of Conics
• 10.7 Plane Curves and Parametric Equations
• 11 Systems of Equations and Inequalities
• 11.1 Systems of Linear Equations: Substitution and Elimination
• 11.2 Systems of Linear Equations: Matrices
• 11.3 Systems of Linear Equations: Determinants
• 11.4 Matrix Algebra
• 11.5 Partial Fraction Decomposition
• 11.6 Systems of Nonlinear Equations
• 11.7 Systems of Inequalities
• 11.8 Linear Programming
• 12 Sequences; Induction; the Binomial Theorem
• 12.1 Sequences
• 12.2 Arithmetic Sequences
• 12.3 Geometric Sequences; Geometric Series
• 12.4 Mathematical Induction
• 12.5 The Binomial Theorem
• 13 Counting and Probability
• 13.1 Counting
• 13.2 Permutations and Combinations
• 13.3 Probability
• 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function
• 14.1 Finding Limits Using Tables and Graphs
• 14.2 Algebra Techniques for Finding Limits
• 14.3 One-Sided Limits; Continuous Functions
• 14.4 The Tangent Problem; The Derivative
• 14.5 The Area Problem; The Integral

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