Precalculus

by Sullivan, Michael

• ISBN13: 9780131431201
• ISBN10: 013143120X
• Edition: 7th
• Format: Hardcover
• Copyright: 2008-01-01
• Publisher: Pearson College Div

Summary

The Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Counting and Probability; A Preview of Calculus; and more. For individuals with an interest in learning Precalculus as it applies to their everyday lives.

Table of Contents

Preface to the Instructor	xi
List of Applications	xvi
Photo Credits	xx
Graphs	1	(48)
Rectangular Coordinates	2	(7)
Graphs of Equations; Circles	9	(13)
Lines	22	(16)
Scatter Diagrams; Linear Curve Fitting	38	(11)
Chapter Review	45	(3)
Chapter Projects	48	(1)
Functions and Their Graphs	49	(74)
Functions	50	(13)
The Graph of a Function	63	(9)
Properties of Functions	72	(11)
Library of Functions; Piecewise-defined Functions	83	(11)
Graphing Techniques: Transformations	94	(13)
Mathematical Models: Constructing Functions	107	(16)
Chapter Review	115	(6)
Chapter Projects	121	(1)
Cumulative Review	122	(1)
Polynomial and Rational Functions	123	(100)
Quadratic Functions and Models	124	(20)
Polynomial Functions	144	(18)
Rational Functions I	162	(11)
Rational Functions II: Analyzing Graphs	173	(15)
Polynomial and Rational Inequalities	188	(6)
The Real Zeros of a Polynomial Function	194	(15)
Complex Zeros; Fundamental Theorem of Algebra	209	(14)
Chapter Review	215	(5)
Chapter Projects	220	(1)
Cumulative Review	221	(2)
Exponential and Logarithmic Functions	223	(100)
Composite Functions	224	(7)
Inverse Functions	231	(13)
Exponential Functions	244	(16)
Logarithmic Functions	260	(13)
Properties of Logarithms	273	(9)
Logarithmic and Exponential Equations	282	(5)
Compound Interest	287	(10)
Exponential Growth and Decay; Newton's Law; Logistic Models	297	(9)
Fitting Data to Exponential, Logarithmic, and Logistic Functions	306	(17)
Chapter Review	314	(6)
Chapter Projects	320	(1)
Cumulative Review	321	(2)
Trigonometric Functions	323	(90)
Angles and Their Measure	324	(14)
Trigonometric Functions: Unit Circle Approach	338	(17)
Properties of the Trigonometric Functions	355	(14)
Graphs of the Sine and Cosine Functions	369	(17)
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions	386	(7)
Phase Shift; Sinusoidal Curve Fitting	393	(20)
Chapter Review	405	(6)
Chapter Projects	411	(1)
Cumulative Review	412	(1)
Analytic Trigonometry	413	(68)
The Inverse Sine, Cosine, and Tangent Functions	414	(11)
The Inverse Trigonometric Functions (continued)	425	(5)
Trigonometric Identities	430	(7)
Sum and Difference Formulas	437	(11)
Double-angle and Half-angle Formulas	448	(9)
Product-to-Sum and Sum-to-Product Formulas	457	(4)
Trigonometric Equations I	461	(6)
Trigonometric Equations II	467	(14)
Chapter Review	475	(4)
Chapter Projects	479	(1)
Cumulative Review	480	(1)
Applications of Trigonometric Functions	481	(54)
Right Triangle Trigonometry; Applications	482	(12)
The Law of Sines	494	(13)
The Law of Cosines	507	(6)
Area of a Triangle	513	(6)
Simple Harmonic Motion; Damped Motion; Combining Waves	519	(16)
Chapter Review	528	(5)
Chapter Projects	533	(1)
Cumulative Review	534	(1)
Polar Coordinates; Vectors	535	(78)
Polar Coordinates	536	(9)
Polar Equations and Graphs	545	(17)
The Complex Plane; De Moivre's Theorem	562	(8)
Vectors	570	(12)
The Dot Product	582	(8)
Vectors in Space	590	(10)
The Cross Product	600	(13)
Chapter Review	607	(4)
Chapter Projects	611	(1)
Cumulative Review	612	(1)
Analytic Geometry	613	(70)
Conies	614	(1)
The Paraboal	615	(10)
The Ellipse	625	(10)
The Hyperbola	635	(14)
Rotation of Axes; General Form of a Conic	649	(9)
Polar Equations of Conics	658	(6)
Plane Curves and Parametric Equations	664	(19)
Chapter Review	678	(3)
Chapter Projects	681	(1)
Cumulative Review	682	(1)
Systems of Equations and Inequalities	683	(100)
Systems of Linear Equations: Substitution and Elimination	684	(16)
Systems of Linear Equations: Matrices	700	(16)
Systems of Linear Equations: Determinants	716	(10)
Matrix Algebra	726	(17)
Partial Fraction Decomposition	743	(8)
Systems of Nonlinear Equations	751	(9)
Systems of Inequalities	760	(9)
Linear Programming	769	(14)
Chapter Review	777	(4)
Chapter Projects	781	(1)
Cumulative Review	782	(1)
Sequences; Induction; The Binomial Theorem	783	(44)
Sequences	784	(9)
Arithmetic Sequences	793	(6)
Geometric Sequences; Geometric Series	799	(12)
Mathematical Induction	811	(4)
The Binomial Theorem	815	(12)
Chapter Review	822	(3)
Chapter Projects	825	(1)
Cumulative Review	826	(1)
Counting and Probability	827	(34)
Sets and Counting	828	(6)
Permutations and Combinations	834	(11)
Probability	845	(16)
Chapter Review	856	(3)
Chapter Projects	859	(1)
Cumulative Review	860	(1)
A Preview of Calculus: The Limit, Derivative, and Integral of a Function	861	(42)
Finding Limits Using Tables and Graphs	862	(5)
Algebra Techniques for Finding Limits	867	(8)
One-sided Limits, Continuous Functions	875	(8)
The Tangent Problem; The Derivative	883	(8)
The Area Problem; The Integral	891	(12)
Chapter Review	898	(4)
Chapter Projects	902	(1)
Appendix A Review	903	(82)
A.1 Algebra Review	903	(10)
A.2 Geometry Review	913	(5)
A.3 Polynomials and Rational Expressions	918	(11)
A.4 Polynomial Division; Synthetic Division	929	(7)
A.5 Solving Equations	936	(11)
A.6 Complex Numbers; Quadratic Equations in the Complex Number System	947	(9)
A.7 Setting Up Equations: Applications	956	(12)
A.8 Interval Notation; Solving Inequalities	968	(9)
A.9 nth Roots; Rational Exponents; Radical Equations	977	(8)
Appendix B Graphing Utilities	985	(1)
B.1 The Viewing Rectangle	985	(2)
B.2 Using a Graphing Utility to Graph Equations	987	(4)
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry	991	(3)
B.4 Using a Graphing Utility to Solve Equations	994	(1)
B.5 Square Screens	995	(1)
B.6 Using a Graphing Utility to Graph Inequalities	996	(2)
B.7 Using a Graphing Utility to Solve Systems of Linear Equations	998	(1)
B.8 Using a Graphing Utility to Graph a Polar Equation	999	(1)
B.9 Using a Graphing Utility to Graph Parametric Equations	1000
Answers	1	(1)
Index	1