Precalculus : Graphs and Models

by Marvin L. Bittinger; Karen Guardino

• ISBN13: 9780201694420
• ISBN10: 0201694425
• Format: Hardcover
• Copyright: 1996-11-01
• Publisher: Addison-Wesley

Table of Contents

Introduction to Graphs and Graphers	1	(20)
Basic Concepts of Algebra
The Real-Number System	20	(5)
Integer Exponents, Scientific Notation, and Order of Operations	25	(7)
Addition, Subtraction, and Multiplication of Polynomials	32	(4)
Factoring	36	(4)
Rational Expressions	40	(9)
Radical Notation and Rational Exponents	49	(9)
Solving Equations	58	(8)
Solving Inequalities	66	(6)
Modeling and Applications	72	(12)
Summary and Review	79	(5)
Graphs, Functions, and Models
Functions, Graphs, and Graphers	84	(14)
Functions and Applications	98	(13)
Linear Functions and Applications	111	(16)
Data Analysis, Curve Fitting, and Linear Regression	127	(8)
Distance, Midpoints, and Circles	135	(5)
Symmetry	140	(7)
Transformations of Functions	147	(11)
The Algebra of Functions	158	(14)
Summary and Review	167	(5)
Polynomial and Rational Functions
Introduction to Polynomial Functions and Complex Numbers	172	(8)
Quadratic Equations and Functions	180	(16)
Polynomial Models and Curve Fitting	196	(12)
Polynomial Division; The Remainder and Factor Theorems	208	(7)
Theorems about OSPF Zeros of Polynomial Functions	215	(9)
Rational Functions	224	(14)
Polynomial and Rational Inequalities	238	(12)
Summary and Review	245	(5)
Exponential and Logarithmic Functions
Inverse Functions	250	(11)
Exponential Functions and Graphs	261	(13)
Logarithmic Functions and Graphs	274	(13)
Properties of Logarithmic Functions	287	(9)
Solving Exponential and Logarithmic Equations	296	(7)
Applications and Models: Growth and Decay	303	(19)
Summary and Review	318	(4)
The Trigonometric Functions
Trigonometric Functions of Acute Angles	322	(11)
Applications of Right Triangles	333	(10)
Trigonometric Functions of Any Angle	343	(15)
Radians, Arc Length, and Angular Speed	358	(14)
Circular Functions: Graphs and Properties	372	(17)
Graphs of Transformed Sine and Cosine Functions	389	(21)
Summary and Review	404	(6)
Trigonometric Identities, Inverse Functions, and Equations
Identities: Pythagorean and Sum and Difference	410	(13)
Identities: Cofunction, Double-Angle, and Half-Angle	423	(8)
Proving Trigonometric Identities	431	(7)
Inverses of the Trigonometric Functions	438	(10)
Solving Trigonometric Equations	448	(16)
Summary and Review	459	(5)
Applications of Trigonometry
The Law of Sines	464	(12)
The Law of Cosines	476	(8)
Complex Numbers: Trigonometric Form	484	(12)
Polar Coordinates and Graphs	496	(9)
Vectors	505	(17)
Summary and Review	518	(4)
Systems and Matrices
Systems of Equations in Two Variables	522	(10)
Systems of Equations in Three or More Variables	532	(8)
Matrices and Systems of Equations	540	(8)
Matrix Operations	548	(12)
Inverses of Matrices	560	(6)
Systems of Inequalities and Linear Programming	566	(11)
Partial Fractions	577	(13)
Summary and Review	585	(5)
Conic Sections
The Parabola	590	(8)
The Circle and the Ellipse	598	(10)
The Hyperbola	608	(9)
Nonlinear Systems of Equations	617	(13)
Summary and Review	625	(5)
Sequences, Series, and Combinatorics
Sequences and Series	630	(11)
Artithmetic Sequences and Series	641	(10)
Geometric Sequences and Series	651	(11)
Mathematical Induction	662	(7)
Combinatorics: Permutations	669	(10)
Combinatorics: Combinations	679	(7)
The Binomial Theorem	686	(9)
Probability	695	(14)
Summary and Review	705	(4)
Appendixes	709
A Determinants and Cramer's Rule	709
B Parametric Equations	716
Answers	A-1
Index of Applications	I-1
Index	I-5