Algebra for College Students

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

• ISBN13: 9780534359447
• ISBN10: 0534359442
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Cengage Learning College

Summary

With an earlier introduction to graphing and functions, this text presents a comprehensive introduction to the topics in intermediate- and college-level algebra. It provides students with the basic skills they'll need to succeed in the next course. As the book progresses, the mathematical language matures, examples grow less structured, and exercises grow more varied.

Table of Contents

Basic Concepts	1	(94)
The Real Number System	2	(12)
Arithmetic and Properties of Real Numbers	14	(16)
Exponents	30	(14)
Scientific Notation	44	(9)
Solving Equations	53	(12)
Using Equations to Solve Problems	65	(12)
More Applications of Equations	77	(17)
Chapter Summary	87	(4)
Chapter Test	91	(3)
Graphs, Equations of Lines, and Functions	94	(92)
The Rectangular Coordinate System	95	(14)
Graphing Linear Equations	109	(14)
Slope of a Nonvertical Line	123	(11)
Writing Equations of Lines	134	(16)
Introduction to Functions	150	(10)
Graphs of Other Functions	160	(26)
Chapter Summary	176	(6)
Chapter Test	182	(1)
Cumulative Review Exercises	183	(3)
Systems of Equations	186	(65)
Solution by Graphing	187	(8)
Solution by Elimination	195	(17)
Solutions of Three Equations in Three Variables	212	(12)
Solution by Matrices	224	(9)
Solution by Determinants	233	(18)
Chapter Summary	247	(2)
Chapter Test	249	(2)
Inequalities	251	(64)
Linear Inequalities	252	(12)
Equations and Inequalities with Absolute Values	264	(14)
Linear Inequalities in Two Variables	278	(10)
Systems of Inequalities	288	(8)
Linear Programming	296	(19)
Chapter Summary	307	(3)
Chapter Test	310	(2)
Cumulative Review Exercises	312	(3)
Polynomials and Polynomial Functions	315	(84)
Polynomials and Polynomial Functions	316	(11)
Adding and Subtracting Polynomials	327	(6)
Multiplying Polynomials	333	(12)
The Greatest Common Factor and Factoring by Grouping	345	(10)
The Difference of Two Squares; the Sum and Difference of Two Cubes	355	(9)
Factoring Trinomials	364	(12)
Summary of Factoring Techniques	376	(5)
Solving Equations by Factoring	381	(18)
Chapter Summary	393	(4)
Chapter Test	397	(2)
Rational Expressions	399	(89)
Rational Functions and Simplifying Rational Expressions	400	(14)
Proportion and Variation	414	(15)
Multiplying and Dividing Rational Expressions	429	(8)
Adding and Subtracting Rational Expressions	437	(12)
Complex Fractions	449	(10)
Equations Containing Rational Expressions	459	(11)
Dividing Polynomials	470	(18)
Chapter Summary	481	(3)
Chapter Test	484	(1)
Cumulative Review Exercises	485	(3)
Rational Exponents and Radicals	488	(73)
Radical Expressions	489	(14)
Applications of Radicals	503	(9)
Radical Equations	512	(9)
Rational Exponents	521	(9)
Simplifying and Combining Radical Expressions	530	(11)
Multiplying and Dividing Radical Expressions	541	(20)
Chapter Summary	553	(5)
Chapter Test	558	(3)
Quadratic Functions and Inequalities	561	(66)
Completing the Square and the Quadratic Formula	562	(13)
Graphs of Quadratic Functions	575	(13)
Complex Numbers	588	(13)
The Discriminant and Equations That Can Be Written in Quadratic Form	601	(7)
Quadratic and Other Nonlinear Inequalities	608	(19)
Chapter Summary	619	(4)
Chapter Test	623	(1)
Cumulative Review Exercises	624	(3)
More Functions and Operations on Functions	627	(71)
Symmetry and Stretchings of Graphs	628	(11)
Piecewise-Defined Functions and the Greatest Integer Function	639	(6)
More Rational Functions	645	(16)
Partial Fractions	661	(8)
Algebra and Composition of Functions	669	(9)
Inverses of Functions	678	(20)
Chapter Summary	692	(4)
Chapter Test	696	(2)
Exponential and Logarithmic Functions	698	(74)
Exponential Functions	699	(14)
Base-e Exponential Functions	713	(8)
Logarithmic Functions	721	(12)
Base-e Logarithms	733	(6)
Properties of Logarithms	739	(11)
Exponential and Logarithmic Equations	750	(22)
Chapter Summary	764	(4)
Chapter Test	768	(2)
Cumulative Review Exercises	770	(2)
Solving Polynomial Equations	772	(43)
The Remainder and Factor Theorems; Synthetic Division	773	(12)
Descartes' Rule of Signs and Bounds on Roots	785	(8)
Rational Roots of Polynomial Equations	793	(9)
Irrational Roots of Polynomial Equations	802	(13)
Chapter Summary	810	(3)
Chapter Test	813	(2)
Conic Sections and Quadratic Systems	815	(63)
The Circle	816	(11)
The Parabola	827	(10)
The Ellipse	837	(11)
The Hyperbola	848	(11)
Solving Simultaneous Second-Degree Equations	859	(19)
Chapter Summary	868	(6)
Chapter Test	874	(1)
Cumulative Review Exercises	875	(3)
Natural Number Functions and Probability	878
The Binomial Theorem	879	(8)
Sequences, Series, and Summation Notation	887	(8)
Arithmetic Sequences	895	(7)
Geometric Sequences	902	(10)
Mathematical Induction	912	(6)
Permutations and Combinations	918	(12)
Probability	930	(8)
Computation of Compound Probabilities	938	(6)
Odds and Mathematical Expectation	944
Chapter Summary	950	(6)
Chapter Test	956	(1)
Cumulative Review Exercises	957
APPENDIX I MATRIX ALGEBRA	A-1	(1)
I.1 Matrix Algebra	A-1	(1)
I.2 Matrix Inversion	A-10	(1)
APPENDIX II TABLES	A-17	(1)
Table A Powers and Roots	A-17	(1)
Table B Base-10 Logarithms	A-18	(1)
Table C Base-e Logarithms	A-19	(1)
APPENDIX III ANSWERS TO SELECTED EXERCISES	A-20	(1)
Index	I-1