A Graphical Approach to College Algebra

by Hornsby, John; Lial, Margaret L.

• ISBN13: 9780321028471
• ISBN10: 0321028473
• Edition: 2nd
• Format: Hardcover
• Copyright: 1998-08-01
• Publisher: Pearson College Div

Summary

This major revision reflects the authors combined years of experience as classroom teachers, and underscores their enthusiasm for the use of the graphing calculator as a teaching tool. Their approach is to present the various classes of functions, examine the nature of its graph, and discuss the analytic solution of equations based on that function. Then, graphical support for the solution is provided with a graphing calculator. Using graphing technology to study math has opened up a new area of error analysis, so the authors have included a What Went Wrong feature to discuss typical errors. Throughout, the accent is on using both analytical and graphical methods to solve interesting applications for various functions. The new edition also includes a reference chapter on basic algebraic concepts for those needing a refresher course.

Table of Contents

Rectangular Coordinates, Functions, and Analysis of Linear Functions	1	(120)
Real Numbers, Logic, and Coordinate System	2	(10)
Introduction to Relations and Functions	12	(14)
Linear Functions	26	(18)
Equations of Lines and Geometric Considerations	44	(15)
Solution of Linear Equations; Analytic Method and Graphical Support	59	(13)
Solution of Linear Inequalities; Analytic Method and Graphical Support	72	(12)
Linear Models	84	(11)
Other Applications of Linear Functions	95	(26)
Summary	110	(2)
Review Exercises	112	(5)
Test	117	(2)
Project Modeling the Growth of the World's Tallest man	119	(2)
Analysis of Graphs of Functions	121	(82)
Graphs of Elementary Functions and Relations	122	(14)
Vertical and Horizontal Shifts of Graphs of Functions	136	(12)
Stretching, Shrinking, and Reflecting Graphs of Functions	148	(11)
The Absolute Value Function: Graphs, Equations, Inequalities, and Applications	159	(14)
Piecewise Defined Functions	173	(9)
Further Topics in the Study of Functions	182	(21)
Summary	195	(1)
Review Exercises	196	(3)
Test	199	(1)
Project Modeling a Trip from One Point to Another, Using a Piecewise Defined Function	200	(3)
Polynomial Functions	203	(112)
Complex Numbers	204	(7)
Quadratic Functions and Their Graphs	211	(12)
Solution of Quadratic Equations and Inequalities	223	(15)
Applications of Quadratic Functions and Models	238	(13)
Higher Degree Polynomial Functions and Their Graphs	251	(17)
Topics in the Theory of Polynomial Functions (I)	268	(11)
Topics in the Theory of Polynomial Functions (II)	279	(9)
Solution of Polynomial Equations and Inequalities and Their Applications	288	(27)
Summary	304	(3)
Review Exercises	307	(5)
Test	312	(1)
Project Creating Your Personal Social Security Polynomial	313	(2)
Reational, Root, and Inverse Functions	315	(80)
Graphs of Rational Functions	315	(18)
Rational Equations, Inequalities, and Applications	333	(15)
Graphs of Root Functions	348	(13)
Root Equations, Inequalities, and Applications	361	(12)
Inverse Functions	373	(22)
Summary	386	(2)
Review Exercises	388	(3)
Test	391	(1)
Project How Rugged is Your Coastline?	392	(3)
Exponential and Logarithmic Functions	395	(71)
Introduction to Exponential Functions	396	(12)
Logarithms and Their Properties	408	(11)
Introduction to Logarithmic Functions	419	(11)
Exponential and Logarithmic Equations and Inequalities	430	(11)
Applications and Modeling with Exponential and Logarithmic Functions	441	(25)
Summary	457	(3)
Review Exercises	460	(3)
Test	463	(1)
Project California's Prison Population	464	(2)
The Conic Sections and Parametric Equations	466	(50)
Circles and Parabolas	467	(14)
Ellipses and Hyperbolas	481	(13)
Summary of the Conic Sections	494	(10)
Parametric Equations	504	(12)
Summary	509	(2)
Review Exercises	511	(2)
Test	513	(1)
Project Modeling the Path of a Bouncing Ball, Using a Piecewise Defined Function	514	(2)
Matrices and Systems of Equations and Inequalities	516	(93)
Systems of Equations	517	(16)
Solution of Linear Systems by the Echelon Method	533	(9)
Solution of Linear Systems by Row Transformations	542	(11)
Properties of Matrices	553	(12)
Determinants and Cramer's Rule	565	(10)
Solution of Linear Systems by Matrix Inverses	575	(9)
Systems of Inequalities and Linear Programming	584	(10)
Partial Fractions	594	(15)
Summary	599	(2)
Review Exercises	601	(3)
Test	604	(2)
Project Finding a Polynomial that Goes Through Any Number of Given Points Using a Matrix	606	(3)
Further Topics in Algebra	609	(65)
Sequences and Series	610	(8)
Arithmetic Sequences and Series	618	(8)
Geometric Sequences and Series	626	(9)
The Binomial Theorem	635	(7)
Mathematical Induction	642	(6)
Counting Theory	648	(9)
Probability	657	(17)
Summary	665	(4)
Review Exercises	669	(2)
Test	671	(1)
Project Using Experimental Probabilities to Simulate the Makeup of a Family	671	(3)
Reference: Basic Algebraic Concepts	674	(1)
Review of Rules for Exponents and Operations with Polynomials	674	(6)
Review of Factoring	680	(6)
Review of Operations with Rational Expressions	686	(7)
Review of Negative and Rational Exponents	693	(7)
Review of Radicals	700
Answers to Selected Exercises	A-1
Index of Applications	I-1
Index	I-5