College Algebra

by Gustafson, R. David; Frisk, Peter D.

• ISBN13: 9780534351595
• ISBN10: 053435159X
• Format: Hardcover
• Copyright: 1997-12-09
• Publisher: Brooks Cole

Table of Contents

1 Basic Concepts	1	(87)
1.1 Sets of Real Numbers	2	(13)
1.2 Integer Exponents and Scientific Notation	15	(12)
1.3 Fractional Exponents and Radicals	27	(14)
1.4 Polynomials	41	(13)
1.5 Factoring Polynomials	54	(10)
1.6 Algebraic Fractions	64	(12)
Problems and Projects	76	(4)
Chapter Summary	80	(6)
Chapter 1 Test	86	(2)
2 Equations and Inequalities	88	(94)
2.1 Linear Equations	89	(9)
2.2 Applications of Linear Equations	98	(11)
2.3 Quadratic Equations	109	(13)
2.4 Applications of Quadratic Equations	122	(6)
2.5 Complex Numbers	128	(11)
2.6 Polynomial and Radical Equations	139	(8)
2.7 Inequalities	147	(14)
2.8 Absolute Value	161	(9)
Problems and Projects	170	(3)
Chapter Summary	173	(5)
Chapter 2 Test	178	(1)
Cumulative Review Exercises	179	(3)
3 The Rectangular Coordinate System and Graphs of Equations	182	(82)
3.1 The Rectangular Coordinate System	183	(16)
3.2 The Slope of a Nonvertical Line	199	(12)
3.3 Writing Equations of Lines	211	(13)
3.4 Graphs of Equations	224	(19)
3.5 Proportion and Variation	243	(8)
Problems and Projects	251	(3)
Chapter Summary	254	(7)
Chapter 3 Test	261	(3)
4 Functions	264	(95)
4.1 Functions and Function Notation	265	(14)
4.2 Quadratic Functions	279	(9)
4.3 Polynomial and Other Functions	288	(11)
4.4 Translating and Stretching Graphs	299	(10)
4.5 Rational Functions	309	(16)
4.6 Operations on Functions	325	(11)
4.7 Inverse Functions	336	(10)
Problems and Projects	346	(3)
Chapter Summary	349	(5)
Chapter 4 Test	354	(2)
Cumulative Review Exercises	356	(3)
5 Exponential and Logarithmic Functions	359	(73)
5.1 Exponential Functions	360	(14)
5.2 Base-e Exponential Functions	374	(9)
5.3 Logarithmic Functions	383	(11)
5.4 Base-e Logarithms	394	(8)
5.5 Properties of Logarithms	402	(11)
5.6 Exponential and Logarithmic Equations	413	(8)
Problems and Projects	421	(4)
Chapter Summary	425	(5)
Chapter 5 Test	430	(2)
6 Solving Polynomial Equations	432	(44)
6.1 The Remainder and Factor Theorems; Synthetic Division	433	(10)
6.2 Descartes' Rule of Signs and Bounds on Roots	443	(9)
6.3 Rational Roots of Polynomial Equations	452	(9)
6.4 Irrational Roots of Polynomial Equations	461	(5)
Problems and Projects	466	(3)
Chapter Summary	469	(4)
Chapter 6 Test	473	(1)
Cumulative Review Exercises	474	(2)
7 Linear Systems	476	(102)
7.1 Systems of Linear Equations	477	(13)
7.2 Gaussian Elimination and Matrix Methods	490	(12)
7.3 Matrix Algebra	502	(15)
7.4 Matrix Inversion	517	(9)
7.5 Determinants	526	(14)
7.6 Partial Fractions	540	(8)
7.7 Graphs of Linear Inequalities	548	(9)
7.8 Linear Programming	557	(10)
Problems and Projects	567	(2)
Chapter Summary	569	(6)
Chapter 7 Test	575	(3)
8 Conic Sections and Quadratic Systems	578	(58)
8.1 The Circle and the Parabola	579	(16)
8.2 The Ellipse	595	(10)
8.3 The Hyperbola	605	(11)
8.4 Solving Simultaneous Second-Degree Equations	616	(7)
Problems and Projects	623	(3)
Chapter Summary	626	(6)
Chapter 8 Test	632	(1)
Cumulative Review Exercises	633	(3)
9 Natural Number Functions and Probability	636	(75)
9.1 The Binomial Theorem	637	(7)
9.2 Sequences, Series, and Summation Notation	644	(8)
9.3 Arithmetic Sequences	652	(7)
9.4 Geometric Sequences	659	(8)
9.5 Mathematical Induction	667	(6)
9.6 Permutations and Combinations	673	(11)
9.7 Probability	684	(7)
9.8 Computation of Compound Probabilities	691	(7)
9.9 Odds and Mathematical Expectation	698	(3)
Problems and Projects	701	(3)
Chapter Summary	704	(5)
Chapter 9 Test	709	(2)
10 The Mathematics of Finance	711
10.1 Compound Interest	712	(10)
10.2 Annuities and Future Value	722	(6)
10.3 Present Value of an Annuity; Amortization	728	(7)
Problems and Projects	735	(2)
Chapter Summary	737	(3)
Chapter 10 Test	740	(1)
Cumulative Review Exercises	740
APPENDIX I A PROOF OF THE BINOMIAL THEOREM	A-1	(2)
APPENDIX II TABLES	A-3	(3)
Table A Powers and Roots	A-3	(1)
Table B Base-10 Logarithms	A-4	(1)
Table C Base-e Logarithms	A-5	(1)
APPENDIX III ANSWERS TO SELECTED EXERCISES	A-6
INDEX	I-1