Precalculus : Functions and Graphs

by Barnett, Raymond A.; Ziegler, Michael R.; Byleen, Karl E.

• ISBN13: 9780070063419
• ISBN10: 0070063419
• Edition: 4th
• Format: Hardcover
• Copyright: 1998-07-30
• Publisher: McGraw-Hill Higher Education

Table of Contents

Preface	ix
Chapter Dependencies	xiv
To the Student	xv
Equations and Inequalities	1	(96)
Linear Equations and Applications	2	(15)
Systems of Linear Equations and Applications	17	(9)
Linear Inequalities	26	(11)
Absolute Value in Equations and Inequalities	37	(10)
Complex Numbers	47	(11)
Quadratic Equations and Applications	58	(15)
Equations Reducible to Quadratic Form	73	(8)
Polynomial and Rational Inequalities	81	(16)
Group Activity: Rates of Change	90	(1)
Review	91	(6)
Graphs and Functions	97	(114)
Basic Tools; Circles	98	(17)
Straight Lines	115	(16)
Functions	131	(16)
Graphing Functions	147	(18)
Combining Functions	165	(17)
Inverse Functions	182	(29)
Group Activity: Mathematical Modeling in Business	198	(2)
Review	200	(7)
1 & 2 Cumulative Review Exercises	207	(4)
Polynomial and Rational Functions	211	(70)
Polynomial Functions and Graphs	213	(12)
Finding Rational Zeros of Polynomials	225	(13)
Approximating Real Zeros of Polynomials	238	(12)
Rational Functions	250	(15)
Partial Fractions	265	(16)
Group Activity: Interpolating Polynomials	273	(2)
Review	275	(6)
Exponential and Logarithmic Functions	281	(58)
Exponential Functions	282	(11)
The Exponential Function with Base e	293	(11)
Logarithmic Functions	304	(9)
Common and Natural Logarithms	313	(10)
Exponential and Logarithmic Equations	323	(16)
Group Activity: Growth of Increasing Functions	333	(1)
Review	333	(3)
3 & 4 Cumulative Review Exercises	336	(3)
Trigonometric Functions	339	(112)
The Wrapping Function	340	(8)
Circular Functions	348	(9)
Angles and Their Measure	357	(9)
Trigonometric Functions	366	(17)
Solving Right Triangles	383	(8)
Graphing Basic Trigonometric Functions	391	(12)
Graphing y = k + A sin (Bx + C) and y = k + A cos (Bx + C)	403	(16)
Graphing More General Tangent, Cotangent, Secant, and Cosecant Functions	419	(8)
Inverse Trigonometric Functions	427	(24)
Group Activity: A Predator-Prey Analysis Involving Mountain Lions and Deer	440	(1)
Review	441	(10)
Trigonometric Identities and Conditional Equations	451	(54)
Basic Identities and Their Use	452	(9)
Sum, Difference, and Cofunction Identities	461	(10)
Double-Angle and Half-Angle Identities	471	(9)
Product-Sum and Sum-Product Identities	480	(5)
Trigonometric Equations	485	(20)
Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C)---A Harmonic Analysis Tool	497	(2)
Review	499	(6)
Additional Topics in Trigonometry	505	(80)
Law of Sines	506	(10)
Law of Cosines	516	(8)
Geometric Vectors	524	(7)
Algebraic Vectors	531	(10)
Polar Coordinates and Graphs	541	(14)
Complex Numbers in Rectangular and Polar Forms	555	(8)
De Moivre's Theorem	563	(22)
Group Activity: Conic Sections and Planetary Orbits	569	(3)
Review	572	(7)
5, 6, & 7 Cumulative Review Exercises	579	(6)
Systems of Equations and Inequalities	585	(74)
Systems of Linear Equations and Augmented Matrices	586	(18)
Gauss-Jordan Elimination	604	(14)
Systems Involving Second-Degree Equations	618	(9)
Systems of Linear Inequalities in Two Variables	627	(13)
Linear Programming	640	(19)
Group Activity: Modeling with Systems of Equations	651	(2)
Review	653	(6)
Matrices and Determinants	659	(64)
Matrices: Basic Operations	660	(14)
Inverse of a Square Matrix	674	(10)
Matrix Equations and Systems of Linear Equations	684	(10)
Determinants	694	(8)
Properties of Determinants	702	(7)
Cramer's Rule	709	(14)
Group Activity: Using Matrices to Find Cost, Revenue, and Profit	714	(1)
Review	715	(5)
8 & 9 Cumulative Review Exercises	720	(3)
Sequences and Series	723	(54)
Sequences and Series	724	(8)
Mathematical Induction	732	(8)
Arithmetic and Geometric Sequences	740	(13)
Binomial Formula	753	(8)
Multiplication Principle, Permutations, and Combinations	761	(16)
Group Activity: Sequences Specified by Recursion Formulas	773	(1)
Review	773	(4)
Additional Topics in Analytic Geometry	777
Conic Sections; Parabola	778	(10)
Ellipse	788	(11)
Hyperbola	799	(12)
Translation of Axes	811	(10)
Parametric Equations	821
Group Activity: Focal Chords	828	(1)
Review	829	(6)
10 & 11 Cumulative Review Exercises	835
Appendix A Basic Algebraic Operations	1	(72)
A-1 Algebra and Real Numbers	2	(10)
A-2 Polynomials: Basic Operations	12	(11)
A-3 Polynomials: Factoring	23	(10)
A-4 Rational Expressions: Basic Operations	33	(9)
A-5 Integer Exponents	42	(9)
A-6 Rational Exponents	51	(6)
A-7 Radicals	57	(16)
Appendix A Group Activity: Rational Number Representations	67	(1)
Appendix A Review	67	(6)
Appendix B Significant Digits	73	(3)
Appendix C Geometric Formulas	76	(3)
Answers	79
Applications Index	1	(2)
Subject Index	3