College Algebra: Concepts Through Functions, 5th edition

Applications Index

F. Foundations: A Prelude to Functions

• F.1 The Distance and Midpoint Formulas
• F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
• F.3 Lines
• F.4 Circles

1. Functions and Their Graphs

• 1.1 Functions
• 1.2 The Graph of a Function
• 1.3 Properties of Functions
• 1.4 Library of Functions; Piecewise-defined Functions
• 1.5 Graphing Techniques: Transformations
• 1.6 Building Mathematical Models from Verbal Descriptions
• 1.7 Building Mathematical Models Using Variation
• Chapter Review
• Chapter Test
• Chapter Projects

2. Linear and Quadratic Functions

• 2.1 Properties of Linear Functions and Linear Models
• 2.2 Building Linear Models from Data
• 2.3 Quadratic Functions and Their Zeros
• 2.4 Properties of Quadratic Functions
• 2.5 Inequalities Involving Quadratic Functions
• 2.6 Building Quadratic Models from Verbal Descriptions and from Data
• 2.7 Complex Zeros of a Quadratic Function
• 2.8 Equations and Inequalities Involving the Absolute Value Function
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

3. Polynomial and Rational Functions

• 3.1 Polynomial Functions
• 3.2 Graphing Polynomial Functions: Models
• 3.3 The Real Zeros of a Polynomial Function
• 3.4 Complex Zeros; Fundamental Theorem of Algebra
• 3.5 Properties of Rational Functions
• 3.6 The Graph of a Rational Function
• 3.7 Polynomial and Rational Inequalities
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

4. Exponential and Logarithmic Functions

• 4.1 Composite Functions
• 4.2 One-to-One Functions; Inverse Functions
• 4.3 Exponential Functions
• 4.4 Logarithmic Functions
• 4.5 Properties of Logarithms
• 4.6 Logarithmic and Exponential Equations
• 4.7 Financial Models
• 4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay Models
• 4.9 Building Exponential, Logarithmic, and Logistic Models from Data
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

5. Analytic Geometry

• 5.1 Conics
• 5.2 The Parabola
• 5.3 The Ellipse
• 5.4 The Hyperbola
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

6. Systems of Equations and Inequalities

• 6.1 Systems of Linear Equations: Substitution and Elimination
• 6.2 Systems of Linear Equations: Matrices
• 6.3 Systems of Linear Equations: Determinants
• 6.4 Matrix Algebra
• 6.5 Partial Fraction Decomposition
• 6.6 Systems of Nonlinear Equations
• 6.7 Systems of Inequalities
• 6.8 Linear Programming
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

7. Sequences; Induction; the Binomial Theorem

• 7.1 Sequences
• 7.2 Arithmetic Sequences
• 7.3 Geometric Sequences; Geometric Series
• 7.4 Mathematical Induction
• 7.5 The Binomial Theorem
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

8. Counting and Probability

• 8.1 Counting
• 8.2 Permutations and Combinations
• 8.3 Probability
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

Appendix A. Review

• A.1 Algebra Essentials
• A.2 Geometry Essentials
• A.3 Polynomials
• A.4 Factoring Polynomials
• A.5 Synthetic Division
• A.6 Rational Expressions
• A.7 nth Roots; Rational Exponents
• A.8 Solving Equations
• A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
• A.10 Interval Notation; Solving Inequalities
• A.11 Complex Numbers

Appendix B. Graphing Utilities

• B.1 The Viewing Rectangle
• B.2 Using a Graphing Utility to Graph Equations
• B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
• B.4 Using a Graphing Utility to Solve Equations
• B.5 Square Screens
• B.6 Using a Graphing Utility to Graph Inequalities
• B.7 Using a Graphing Utility to Solve Systems of Linear Equations

Answers

Challenge Problem Solutions

Subject Index