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A Graphical Approach to Precalculus,9780321028488
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A Graphical Approach to Precalculus

by ;
Edition:
2nd
ISBN13:

9780321028488

ISBN10:
0321028481
Format:
Hardcover
Pub. Date:
10/1/1998
Publisher(s):
Pearson College Div
List Price: $112.00
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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


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