Precalculus: Functions and Graphs

by Dugopolski, Mark

• ISBN13: 9780201742060
• ISBN10: 0201742063
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Addison Wesley

Summary

Building on Mark Dugopolski's name, this graphing optional text is designed for the one or two semester precalculus course. With faster pacing and less review, this is an excellent choice for those students going on to calculus.

Table of Contents

Equations, Inequalities, and Modeling

Equations in One Variable

Equations and Graphs in Two Variables

Scatter Diagrams and Curve Fitting

Constructing Models to Solve Problems

Quadratic Equations

Linear and Absolute Value Inequalities

Quadratic and Rational Inequalities

Functions and Graphs

Functions

Graphs of Relations and Functions

Families of Functions: Transformations and Symmetry

Operations with Functions

Inverse Functions

Constructing Functions with Variation

Polynomial and Rational Functions

Linear Functions

Quadratic Functions

Complex Numbers

Zeros of Polynomial Functions

The Theory of Equations

Graphs of Polynomial Functions

Graphs of Rational Functions

Exponential and Logarithmic Functions

Exponential Functions and Their Applications

Logarithmic Functions and Their Applications

Properties of Logarithms

More Equations and Applications

The Trigonometric Functions

Angles and Their Measurements

The Sine and Cosine Functions

The Graphs of the Sine and Cosine Functions

The Other Trigonometric Functions and Their Graphs

The Inverse Trigonometric Functions

Right Triangle Trigonometry

Trigonometric Identities and Conditional Equations

Basic Identities

Verifying Identities

Sum and Difference Identities

Double-Angle and Half-Angle Identities

Product and Sum Identities

Conditional Trigonometric Equations

Applications of Trigonometry

The Law of Sines

The Law of Cosines

Vectors

Trigonometric Form of Complex Numbers

Powers and Roots of Complex Numbers

Polar Equations

Parametric Equations

Systems of Equations and Inequalities

Systems of Linear Equations in Two Variables

Systems of Linear Equations in Three Variables

Nonlinear Systems of Equations

Partial Fractions

Inequalities and Systems of Inequalities in Two Variables

Linear Programming

Matrices and Determinants

Solving Linear Systems Using Matrices

Operations with Matrices

Multiplication of Matrices

Inverses of Matrices

Solution of Linear Systems in Two Variables Using Determinants

Solution of Linear Systems in Three Variables Using Determinants

The Conic Sections

The Parabola

The Ellipse and the Circle

The Hyperbola

Rotation of Axes

Polar Equations of the Conics

Sequences, Series and Probability

Sequences

Series

Geometric Sequences and Series

Counting and Permutations

Combinations, Labeling, and the Binomial Theorem

Probability

Mathematical Induction

Appendix A

Real Numbers and Their Properties

Exponents and Radicals

Polynomials

Factoring Polynomials

Rational Expressions

Appendix B

Table of Contents provided by Publisher. All Rights Reserved.