Algebra and Trigonometry : Graphs and Models

by Bittinger, Marvin L.; Ellenbogen, David; Beecher, Judith A.; Penna, Judith A.

• ISBN13: 9780201616736
• ISBN10: 0201616734
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-08-01
• Publisher: Addison-Wesley

Table of Contents

Introduction to Graphs and the Graphing Calculator	1	(13)
Basic Concepts of Algebra
The Real-Number System	14	(6)
Integer Exponents, Scientific Notation, and Order of Operations	20	(8)
Addition, Subtraction, and Multiplication of Polynomials	28	(4)
Factoring	32	(5)
Rational Expressions	37	(8)
Radical Notation and Rational Exponents	45	(9)
The Basics of Equation Solving	54	(10)
Summary and Review	59	(5)
Graphs, Functions, and Models
Functions, Graphs, and Graphers	64	(14)
Linear Functions, Slope, and Applications	78	(18)
Modeling: Data Analysis, Curve Fitting, and Linear Regression	96	(10)
More on Functions	106	(16)
Symmetry and Transformations	122	(16)
Variation and Applications	138	(9)
Distance, Midpoints, and Circles	147	(13)
Summary and Review	153	(7)
Functions and Equations: Zeros and Solutions
Zeros of linear Functions and Models	160	(11)
The Complex Numbers	171	(7)
Zeros of Quadratic Functions and Models	178	(13)
Analyzing Graphs of Quadratic Functions	191	(11)
Modeling: Data Analysis, Curve Fitting, and Quadratic Regression	202	(6)
Zeros and More Equation Solving	208	(6)
Solving Inequalities	214	(10)
Summary and Review	219	(5)
Polynomial and Rational Functions
Polynomial Functions and Modeling	224	(13)
Polynomial Division; The Remainder and Factor Theorems	237	(9)
Theorems about Zeros of Polynomial Functions	246	(8)
Rational Functions	254	(16)
Polynomial and Rational Inequalities	270	(12)
Summary and Review	278	(4)
Exponential and Logarithmic Functions
Composite and Inverse Functions	282	(15)
Exponential Functions and Graphs	297	(13)
Logarithmic Functions and Graphs	310	(14)
Properties of Logarithmic Functions	324	(9)
Solving Exponential and Logarithmic Equations	333	(8)
Applications and Models: Growth and Decay	341	(19)
Summary and Review	356	(4)
The Trigonometric Functions
Trigonometric Functions of Acute Angles	360	(11)
Applications of Right Triangles	371	(9)
Trigonometric Functions of Any Angle	380	(15)
Radians, Arc Length, and Angular Speed	395	(14)
Circular Functions: Graphs and Properties	409	(17)
Graphs of Transformed Sine and Cosine Functions	426	(20)
Summary and Review	440	(6)
Trigonometric Identities, Inverse Functions, and Equations
Identities: Pythagorean and Sum and Difference	446	(13)
Identities: Cofunction, Double-Angle, and Half-Angle	459	(9)
Proving Trigonometric Identities	468	(6)
Inverses of the Trigonometric Functions	474	(11)
Solving Trigonometric Equations	485	(17)
Summary and Review	497	(5)
Applications of Trigonometry
The Law of Sines	502	(12)
The Law of Cosines	514	(9)
Complex Numbers: Trigonometric Form	523	(12)
Polar Coordinates and Graphs	535	(8)
Vectors and Applications	543	(8)
Vector Operations	551	(21)
Summary and Review	565	(7)
Systems of Equations and Matrices
Systems of Equations in Two Variables	572	(11)
Systems of Equations in Three Variables	583	(9)
Matrices and Systems of Equations	592	(8)
Matrix Operations	600	(11)
Inverses of Matrices	611	(6)
Systems of Inequalities and Linear Programming	617	(10)
Partial Fractions	627	(13)
Summary and Review	633	(7)
Conic Sections
The Parabola	640	(8)
The Circle and the Ellipse	648	(9)
The Hyperbola	657	(10)
Nonlinear Systems of Equations	667	(15)
Summary and Review	677	(5)
Sequences, Series, and Combinatorics
Sequences and Series	682	(9)
Arithmetic Sequences and Series	691	(9)
Geometric Sequences and Series	700	(10)
Mathematical Induction	710	(6)
Combinatorics: Permutations	716	(9)
Combinatorics: Combinations	725	(8)
The Binomial Theorem	733	(8)
Probability	741	(14)
Summary and Review	751	(4)
Appendixes
A Descartes' Rule of Signs	755	(2)
B Determinants and Cramer's Rule	757	(8)
C Parametric Equations	765
Answers	1	(1)
Index	1	(12)
Index of Applications	13