Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry

FOUNDATIONS: A PRELUDE TO FUNCTIONS

F.1 The Distance and Midpoint Formulas

F.2 Graphs of Equations; Intercepts; Symmetry

F.3 Lines

F.4 Circles

 

Chapter 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 Mathematical Models: Constructing Functions

Chapter Review

Chapter Test

Chapter Projects

 

Chapter 2 Linear and Quadratic Functions

2.1 Properties of Linear Functions

2.2 Building Linear Functions from Data; Direct Variation

2.3 Quadratic Functions and Their Real Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Quadratic Models; Building Quadratic Functions From Data

2.7 Complex Zeros of a Quadratic Function

2.8 Equations and Inequalities Involving the Absolute Value Function

Chapter Review

Chapter Test

Chapter Projects

      Cumulative Review

 

Chapter 3       Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 Properties of Rational Functions

3.3 The Graph of a Rational Function; Inverse and Joint Variation

3.4 Polynomial and Rational Inequalities

3.5 The Real Zeros of a Polynomial Function

3.6 Complex Zeros: Fundamental Theorem of Algebra

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 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 Compound Interest

4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay

4.9 Building Exponential, Logarithmic, and Logistic Functions from Data

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

 

Chapter 5       Trigonometric Functions

5.1 Angles and Their Measure

5.2 Right Triangle Trigonometry

5.3 Computing the Values of Trigonometric Functions of Acute Angles

5.4 Trigonometric Functions of General Angles

5.5 Unit Circle Approach: Properties of the Trigonometric Functions

5.6 Graphs of the Sine and Cosine Functions

5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

5.8 Phase Shift; Building Sinusoidal Functions from Data

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

 

Chapter 6       Analytic Trigonometry

6.1 The Inverse Sine, Cosine, and Tangent Functions

6.2 The Inverse Trigonometric Functions (continued)

6.3 Trigonometric Identities

6.4 Sum and Difference Formulas

6.5 Double-Angle and Half-Angle Formulas

6.6 Product-to-Sum and Sum-to-Product Formulas

6.7 Trigonometric Equations (I)

6.8 Trigonometric Equations (II)

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 7       Applications of Trigonometric Functions

7.1 Applications Involving Right Triangles

7.2 Law of Sines

7.3 Law of Cosines

7.4 Area of a Triangle

7.5 Simple Harmonic Motion; Damped Motion; Combining Waves

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 8       Polar Coordinates; Vectors

8.1 Polar Coordinates

8.2 Polar Equations and Graphs

8.3 The Complex Plane; DeMoivre’s Theorem

8.4 Vectors

8.5 The Dot Product

8.6 Vectors in Space

8.7 The Cross Product

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

 

Chapter 9       Analytic Geometry

9.1 Conics

9.2 The Parabola

9.3 The Ellipse

9.4 The Hyperbola

9.5 Rotation of Axes; General Form of a Conic

9.6 Polar Equations of Conics

9.7 Plane Curves and Parametric Equations

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 10       Systems of Equations and Inequalities

10.1 Systems of Linear Equations: Substitution and Elimination

10.2 Systems of Linear Equations: Matrices

10.3 Systems of Linear Equations: Determinants

10.4 Matrix Algebra

10.5 Partial Fraction Decomposition

10.6 Systems of Nonlinear Equations

10.7 Systems of Inequalities

10.8 Linear Programming

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

Chapter 11       Sequences; Induction; The Binomial Theorem

11.1 Sequences

11.2 Arithmetic Sequences

11.3 Geometric Sequences; Geometric Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

Chapter Review

Chapter Test

Chapter Projects

Cumulative Review

 

 

Chapter 12       Counting and Probability

12.1 Sets and Counting

12.2 Permutations and Combinations

12.3 Probability

Chapter Review

Chapter Test

Chapter Project

Cumulative Review

 

Chapter 13  A Preview of Calculus: The Limit, Derivative, and Integral of a Function

13.1 Finding Limits Using Tables and Graphs

13.2 Algebra Techniques for Finding Limits

13.3 One-sided Limits; Continuous Functions

13.4 The Tangent Problem; The Derivative

13.5 The Area Problem; The Integral

Chapter Review

Chapter Test

Chapter Project

 

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 Algebraically

A.9 Interval Notation; Solving Inequalities

A.10 Problem Solving: Applications of Linear Equations

A.11 Complex Numbers

 

Appendix B Graphing Utilities

B.1 The Viewing Rectangle

B.2 Graphing Equations in Two Variables

B.3 Locating Intercepts and Checking for Symmetry

B.4 Solving Equations Using a Graphing Utility

B.5 Square Screens

B.6 Graphing Inequalities in Two Variables

B.7 Solving Systems of Linear Equations

B.8 Graphing a Polar Equation

B.9 Graphing Parametric Equations

 

Answers

Index