Beginning and Intermediate Algebra

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

• ISBN13: 9780534359430
• ISBN10: 0534359434
• Format: Hardcover
• Copyright: 1999-08-01
• Publisher: Cengage Learning

Table of Contents

1 Real Numbers and Their Basic Properties	1	(89)
1.1 Real Numbers and Their Graphs	2	(12)
1.2 Fractions	14	(17)
1.3 Exponents and Order of Operations	31	(13)
1.4 Adding and Subtracting Real Numbers	44	(12)
1.5 Multiplying and Dividing Real Numbers	56	(8)
1.6 Algebraic Expressions	64	(9)
1.7 Properties of Real Numbers	73	(8)
Projects	81	(1)
Chapter Summary	82	(6)
Chapter Test	88	(2)
2 Equations and Inequalities	90	(74)
2.1 Solving Equations by Addition and Subtraction	91	(11)
2.2 Solving Equations by Multiplication and Division	102	(8)
2.3 Solving More Equations	110	(9)
2.4 Simplifying Expressions to Solve Equations	119	(8)
2.5 Applications of Equations	127	(12)
2.6 Formulas	139	(7)
2.7 Solving Inequalities	146	(9)
Projects	155	(2)
Chapter Summary	157	(4)
Chapter Test	161	(1)
Cumulative Review Exercises	162	(2)
3 Graphing and Solving Systems of Equations and Inequalities	164	(93)
3.1 The Rectangular Coordinate System	165	(14)
3.2 Graphing Linear Equations	179	(15)
3.3 Solving Systems of Equations by Graphing	194	(13)
3.4 Solving Systems of Equations by Substitution	207	(6)
3.5 Solving Systems of Equations by Addition	213	(8)
3.6 Applications of Systems of Equations	221	(13)
3.7 Solving Systems of Linear Inequalities	234	(15)
Project	249	(1)
Chapter Summary	250	(5)
Chapter Test	255	(2)
4 Polynomials	257	(78)
4.1 Natural-Number Exponents	258	(9)
4.2 Zero and Negative-Integer Exponents	267	(7)
4.3 Scientific Notation	274	(7)
4.4 Polynomials	281	(13)
4.5 Adding and Subtracting Polynomials	294	(8)
4.6 Multiplying Polynomials	302	(11)
4.7 Dividing Polynomials by Monomials	313	(7)
4.8 Dividing Polynomials by Polynomials	320	(7)
Project	327	(1)
Chapter Summary	327	(4)
Chapter Test	331	(1)
Cumulative Review Exercises	332	(3)
5 Factoring Polynomials	335	(57)
5.1 Factoring Out the Greatest Common Factor	336	(9)
5.2 Factoring by Grouping	345	(5)
5.3 Factoring the Difference of Two Squares	350	(6)
5.4 Factoring Trinomials with Lead Coefficients of 1	356	(11)
5.5 Factoring General Trinomials	367	(9)
5.6 Summary of Factoring Techniques	376	(4)
5.7 Problem Solving	380	(7)
Project	387	(1)
Chapter Summary	388	(3)
Chapter Test	391	(1)
6 Proportion and Rational Expressions	392	(82)
6.1 Ratios	393	(7)
6.2 Proportions and Similar Triangles	400	(13)
6.3 Simplifying Fractions	413	(8)
6.4 Multiplying and Dividing Fractions	421	(10)
6.5 Adding and Subtracting Fractions	431	(13)
6.6 Complex Fractions	444	(7)
6.7 Solving Equations That Contain Fractions	451	(8)
6.8 Applications of Equations That Contain Fractions	459	(6)
Projects	465	(1)
Chapter Summary	466	(4)
Chapter Test	470	(1)
Cumulative Review Exercises	471	(3)
7 More Equations, Inequalities, and Factoring	474	(79)
7.1 Review of Equations and Inequalities	475	(16)
7.2 Equations Containing Absolute Values	491	(6)
7.3 Inequalities Containing Absolute Values	497	(6)
7.4 Review of Factoring	503	(14)
7.5 Factoring the Sum and Difference of Two Cubes	517	(6)
7.6 Review of Rational Expressions	523	(16)
7.7 Synthetic Division	539	(7)
Projects	546	(2)
Chapter Summary	548	(3)
Chapter Test	551	(2)
8 Writing Equations of Lines; Variation	553	(86)
8.1 A Review of the Rectangular Coordinate System	554	(11)
8.2 Slope of a Nonvertical Line	565	(12)
8.3 Writing Equations of Lines	577	(15)
8.4 A Review of Functions	592	(11)
8.5 Graphs of Nonlinear Functions	603	(15)
8.6 Variation	618	(10)
Projects	628	(2)
Chapter Summary	630	(5)
Chapter Test	635	(2)
Cumulative Review Exercises	637	(2)
9 Rational Exponents and Radicals	639	(73)
9.1 Radical Expressions	640	(14)
9.2 Applications of Radicals	654	(9)
9.3 Radical Equations	663	(9)
9.4 Rational Exponents	672	(9)
9.5 Simplifying and Combining Radical Expressions	681	(11)
9.6 Multiplying and Dividing Radical Expressions	692	(10)
Projects	702	(2)
Chapter Summary	704	(5)
Chapter Test	709	(3)
10 Quadratic Functions, Inequalities, and Algebra of Functions	712	(88)
10.1 Completing the Square and the Quadratic Formula	713	(13)
10.2 Graphs of Quadratic Functions	726	(13)
10.3 Complex Numbers	739	(13)
10.4 The Discriminant and Equations That Can Be Written in Quadratic Form	752	(7)
10.5 Quadratic and Other Nonlinear Inequalities	759	(9)
10.6 Algebra and Composition of Functions	768	(9)
10.7 Inverses of Functions	777	(11)
Projects	788	(2)
Chapter Summary	790	(5)
Chapter Test	795	(2)
Cumulative Review Exercises	797	(3)
11 Exponential and Logarithmic Functions	800	(73)
11.1 Exponential Functions	801	(14)
11.2 Base-e Exponential Functions	815	(8)
11.3 Logarithmic Functions	823	(12)
11.4 Base-e Logarithms	835	(6)
11.5 Properties of Logarithms	841	(11)
11.6 Exponential and Logarithmic Equations	852	(12)
Projects	864	(2)
Chapter Summary	866	(4)
Chapter Test	870	(3)
12 More Graphing and Conic Sections	873	(55)
12.1 The Circle and the Parabola	874	(15)
12.2 The Ellipse	889	(11)
12.3 The Hyperbola	900	(12)
12.4 Piecewise-Defined Functions and the Greatest Integer Function	912	(8)
Project	920	(1)
Chapter Summary	921	(3)
Chapter Test	924	(1)
Cumulative Review Exercises	925	(3)
13 More on Systems of Equations and Inequalities	928	(63)
13.1 Solutions of Two Equations in Two Variables	929	(14)
13.2 Solutions of Three Equations in Three Variables	943	(12)
13.3 Solution by Matrices	955	(9)
13.4 Solution by Determinants	964	(12)
13.5 Solving Simultaneous Second-Degree Equations and Inequalities	976	(8)
Projects	984	(2)
Chapter Summary	986	(3)
Chapter Test	989	(2)
14 Miscellaneous Topics	991
14.1 The Binomial Theorem	992	(7)
14.2 The nth Term of a Binomial Expansion	999	(4)
14.3 Arithmetic Sequences	1003	(9)
14.4 Geometric Sequences	1012	(9)
14.5 Infinite Geometric Sequences	1021	(4)
14.6 Permutations and Combinations	1025	(11)
Projects	1036	(3)
Chapter Summary	1039	(4)
Chapter Test	1043	(1)
Cumulative Review Exercises	1043
APPENDIX I SYMMETRIES OF GRAPHS	A-1	(5)
APPENDIX II TABLES	A-6	(3)
Table A Powers and Roots	A-6	(1)
Table B Base-10 Logarithms	A-7	(1)
Table C Base-e Logarithms	A-8	(1)
APPENDIX III ANSWERS TO SELECTED EXERCISES	A-9
INDEX	I-1