A Graphical Approach to Precalculus

by Hornsby, E. John; Lial, Margaret L.

• ISBN13: 9780321028488
• ISBN10: 0321028481
• Edition: 2nd
• Format: Hardcover
• Copyright: 1998-10-01
• Publisher: Pearson College Div

Summary

This book is the culmination of many years of teaching experience with the graphing calculator. In it the authors treat the standard topics of precalculus solving analytically, confirming graphically, and motivating through applications. Throughout the first five chapters, the authors present the various classes of functions studied in a standard precalculus text. Chapter One introduces functions and relations, using the linear function as the basis for the presentation. In this chapter, the authors introduce the following approach which is used throughout the next four chapters: after introducing a class of function the nature of its graph is examined, then the analytic solution of equations based on that functionis discussed. Students are then shown how to provide graphical support for solutions using a graphing calculator. Having established these two methods of solving equations, the authors move on to the analytic methods of solving the associated inequalities. Students then learn how the analytic solutions of these inequalities can also be supported graphically. Finally, once the student has a feel for the particular class of function under consideration, the authors use analytic and graphical methods to solve interesting applications involving that function. By consistently using this approach with all the different classes of functions, students become aware that the authors are always following the same general procedure, and just applying that procedure to a new kind of function. Throughout the text, the authors emphasize the power of technology but provide numerous warnings on its limitations: the authors stress that it is only through understanding the mathematical concepts that students can fully appreciate the power of graphing calculators and use technology appropriately.

Table of Contents

Rectangular Coordinates, Functions, and Analysis of linear Functions	1	(120)
Real Numbers, Logic, and Coordinate Systems	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	193	(3)
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)
Rational, 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 Findings Polynomial that goes Through any Number of Given Points Using A Matrix	606	(3)
The Trigonometric Functions and Applications	609	(94)
Angles and their Measures	610	(13)
The Circular Functions	623	(8)
The trigonometric Functions and the Fundamental Identities	631	(12)
Evaluating Trigonometric Functions	643	(11)
Applications of Right Triangle Trigonometry	654	(13)
Analysis of the Sine and Cosine Functions	667	(15)
Analysis of Other Circular Functions	682	(21)
Summary	692	(5)
Review Exercises	697	(3)
Test	700	(1)
Project What Time is Sunset?	701	(2)
Trigonometric Identities and Equations	703	(60)
Identities: Analytic Verification and Graphical Support	704	(9)
Further Identities	713	(17)
The Inverse Circular Functions	730	(13)
Trigonometric Equations and Inequalities	743	(5)
Further Equations and Inequalities	748	(15)
Summary	755	(2)
Review Exercises	757	(3)
Test	760	(1)
Project Modelling Damped Pendulum	760	(3)
Applications of Trigonometry; Vectors	763	(66)
The Law of Sines	764	(11)
The Law of Cosines and Area Formulas	775	(9)
Vectors and Their Applications	784	(11)
Trigonometric (Polar) Form of Complex Numbers	795	(9)
Powers and Roots of Complex Numbers	804	(6)
Polar Coordinates and Polar Equations	810	(19)
Summary	820	(3)
Review Exercises	823	(3)
Test	826	(1)
Project When is a Circle Really a Polygon? Investigating Polar Circles	827	(2)
Further Topics in Algebra	829	(65)
Sequences and Series	830	(8)
Arithmetic Sequences and Series	838	(7)
Geometric Sequences and Series	845	(10)
The Binomial Theorem	855	(7)
Mathematical Induction	862	(6)
Counting Theory	868	(9)
Probability	877	(17)
Summary	885	(4)
Review Exercises	889	(2)
Test	891	(1)
Project Using Experimental Probabilities to Simulate The Makeup of a Family	891	(3)
Reference: Basic Algebraic Concepts	894
Review of Rules for Exponents and Operations with Polynomials	894	(6)
Review of Factoring	900	(6)
Review of Operations with Rational Expressions	906	(7)
Review of Negative and Rational Exponents	913	(7)
Review of Radicals	920
Answers To Selected Exercises	A-1	(1)
Index of Applications	I-1	(1)
Index	I-6