Modeling, Functions, and Graphs: Algebra for College Students

by Bruce Yoshiwara; Katherine Yoshiwara; Irving Drooyan

• ISBN13: 9780534945602
• ISBN10: 0534945600
• Edition: 2nd
• Format: Paperback
• Copyright: 1995-12-19
• Publisher: Brooks Cole

Table of Contents

Preface	ix
1 FUNDAMENTALS	1	(67)
1.1 Introduction	1	(6)
1.2 Algebraic Expressions	7	(10)
1.3 Linear Equations	17	(9)
1.4 Other Types of Equations	26	(10)
1.5 Facts from Geometry	36	(11)
1.6 Graphs	47	(16)
Chapter 1 Review	63	(5)
2 LINEAR MODELS	68	(69)
2.1 Some Examples of Linear Models	68	(9)
2.2 Slope	77	(12)
2.3 Using a Graphing Calculator	89	(10)
2.4 Equations of Lines	99	(10)
2.5 Additional Properties of Lines	109	(9)
2.6 Graphical Solution of Equations and Inequalities	118	(15)
Chapter 2 Review	133	(4)
3 APPLICATIONS OF LINEAR MODELS	137	(65)
3.1 Systems of Linear Equations in Two Variables	137	(11)
3.2 Solution of Systems by Algebraic Methods	148	(8)
3.3 Systems of Linear Equations in Three Variables	156	(13)
3.4 Linear Approximations	169	(10)
3.5 Linear Inequalities in Two Variables	179	(8)
3.6 Linear Programming	187	(12)
Chapter 3 Review	199	(3)
4 QUADRATIC MODELS	202	(61)
4.0 Skills Review	202	(1)
4.1 Some Examples of Quadratic Models	203	(7)
4.2 Solving Quadratic Equations	210	(8)
4.3 Completing the Square; Quadratic Formula	218	(10)
4.4 Graphing Parabolas	228	(11)
4.5 Quadratic Inequalities	239	(10)
4.6 Problem Solving	249	(12)
Chapter 4 Review	261	(2)
5 FUNCTIONS AND THEIR GRAPHS	263	(74)
5.1 Definitions and Notation	263	(12)
5.2 Graphs of Functions	275	(12)
5.3 Some Basic Graphs	287	(13)
5.4 Direct and Inverse Variation	300	(13)
5.5 Functions as Mathematical Models	313	(19)
Chapter 5 Review	332	(5)
6 POWERS AND ROOTS	337	(55)
6.1 Laws of Exponents	337	(7)
6.2 Integer Exponents	344	(9)
6.3 nth Roots and Irrational Numbers	353	(9)
6.4 Rational Exponents	362	(6)
6.5 Radicals	368	(9)
6.6 Radical Equations and the Distance Formula	377	(12)
Chapter 6 Review	389	(3)
7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS	392	(59)
7.1 Exponential Growth and Decay	392	(12)
7.2 Exponential Functions	404	(11)
7.3 Logarithms	415	(7)
7.4 Logarithmic Functions	422	(10)
7.5 Properties of Logarithms	432	(9)
7.6 The Natural Base	441	(8)
Chapter 7 Review	449	(2)
8 POLYNOMIAL AND RATIONAL FUNCTIONS	451	(67)
8.1 Polynomial Functions	451	(12)
8.2 Graphing Polynomial Functions	463	(7)
8.3 Rational Functions	470	(14)
8.4 Operations on Algebraic Fractions	484	(9)
8.5 More Operations on Algebraic Fractions	493	(10)
8.6 Equations That Include Algebraic Fractions	503	(10)
Chapter 8 Review	513	(5)
9 SEQUENCES AND SERIES	518	(45)
9.1 Sequences	518	(8)
9.2 Arithmetic and Geometric Sequences	526	(8)
9.3 Series	534	(8)
9.4 Sigma Notation and Infinite Geometric Series	542	(6)
9.5 Binomial Expansion	548	(13)
Chapter 9 Review	561	(2)
10 ADDITIONAL TOPICS	563	(57)
10.1 Further Graphing Techniques	563	(10)
10.2 Conic Sections	573	(17)
10.3 Translated Conics	590	(14)
10.4 Inverse Functions	604	(7)
10.5 Solution of Linear Systems Using Matrices	611	(7)
Chapter 10 Review	618	(2)
APPENDIX	620	(83)
A.1 Subsets and Properties of the Real Numbers	620	(2)
A.2 Review of Products and Factoring	622	(8)
A.3 Complex Numbers	630	(6)
Answers	636	(63)
Index	699	(4)
A STATISTICS SAMPLER	703