Exploring Introductory and Intermediate Algebra A Graphing Approach

by Aufmann, Richard N.; Lockwood, Joanne; Boswell, Laurie

• ISBN13: 9780618156863
• ISBN10: 0618156860
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-07-01
• Publisher: Cengage Learning

Summary

Intended for a one- or two-semester combined elementary and intermediate algebra course,Exploring Introductory and Intermediate Algebra: A Graphing Approachis designed to assist students in making connections between mathematics and its applications. Its goal is to develop a student's mathematical skills through appropriate use of applications and to use technology to establish links between abstract mathematical concepts and visual or concrete representations. The provenAufmann Interactive Method(AIM) ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains one or more sets of matched-pair examples encouraging students to interact with the text. The first example in each set is completely worked out; the second example, called 'You Try It,' prompts students to practice concepts at the time they are presented in the text.Complete worked-out solutionsto these examples in an appendix at the end of the book help students by providing immediate feedback, concept reinforcement, and identification of mistakes to prevent frustration. Technology is integrated throughout the text to assist students in making connections between abstract mathematical concepts and a concrete representation provided by technology. This is one way in which students are encouraged to think about and use multiple representations of a concept. The inclusion of technology also facilitates computation in order to focus on analysis rather than manipulation and enables students to examine concepts that would be too difficult or time consuming if the technology were not available. Calculator Notesthroughout offer tips on using the graphing calculator and See Appendix B notes in student text margin refer students to the graphing calculator appendix for detailed TI-83 and TI-83+ keystroke information. Eduspace, powered by Blackboard, for the Aufmann/Lockwood/BoswellExploring Introductory and Intermediate Algebracourse features algorithmic exercises and test bank content in question pools.

Table of Contents

Note: Each chapter begins with a Prep Test and includes a Chapter Summary, Chapter Review Exercises, and a Chapter Test

Chapters 2–10 conclude with Cumulative Review Exercises

Fundamental Concepts

Problem Solving

Sets

Operations on Integers

Operations on Rational Numbers

Evaluating Variable Expressions

Simplifying Variable Expressions

Introduction to Functions and Relations

Rectangular Coordinates and Graphs

Relations and Functions

Properties of Functions

First-Degree Equations and Inequalities

Solving First-Degree Equations

Applications of First-Degree Equations

Applications to Geometry

Inequalities in One Variable

Absolute Value Equations and Inequalities

Linear Functions

Slopes and Graphs of Linear Functions

Finding Equations of Straight Lines

Linear Regression

Linear Inequalities in Two Variables

Systems of Linear Equations and Inequalities

Solving Systems of Linear Equations by Graphing and by the Substitution Method

Solving Systems of Linear Equations by the Addition Method

Solving Systems of Linear Equations Using Matrices

Systems of Linear Inequalities

Polynomials

Operations on Monomials and Scientific Notation

Addition and Subtraction of Polynomials

Multiplication and Division of Polynomials

Factoring

Common Factors of a Polynomial

Factoring Trinomials of the Form ax2 + bx + c

Special Factoring

Solving Equations by factoring

Rational Expressions and Equations

Introduction to Rational Expressions

Operations on Rational Expressions

Rational Equations

Proportions and Similar Triangles

Radical Expressions and Rational Exponents

Rational Exponents and Radical Expressions

Simplifying Radical Expressions

The Pythagorean Theorem

Operations on Radical Expressions

Radical Functions

Solving Radical Equations

Complex Numbers

Quadratic Functions and Quadratic Inequalities

Introduction to Quadratic Equations

Solving Quadratic Equations by Taking Square Roots and by Completing the Square

Solving Quadratic Equations by Using the Quadratic Formula and by Graphing

Equations That Are Quadratic in Form

Quadratic Functions

Quadratic Inequalities

Exponential and Logarithmic Functions

Algebra of Functions

Inverse Functions

Exponential Functions

Exponential Models and Exponential Regression

Logarithmic Functions

Properties of Logarithms

Exponential and Logarithmic Equations

Review of Introductory Algebra Topics

Variable Expressions

Equations and Inequalities

Linear Equatinos in Two Variables

Polynomials

Keystroke Guide for the TI-83 and TI-83 Plus

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