Algebra for College Students

by Aufmann

• ISBN13: 9780395692837
• ISBN10: 0395692830
• Format: Hardcover
• Publisher: Houghton Mifflin Company

Table of Contents

Preface	xv
To the Student	xxv
Equations and Inequalities	1	(76)
Variable Expressions	3	(19)
Properties of Real Numbers	3	(3)
Set operations and interval notation	6	(5)
Evaluate variable expressions	11	(2)
Simplify variable expressions	13	(1)
Simplify radical expressions	14	(2)
Translate verbal expressions into variable expressions	16	(6)
Equations	22	(14)
Solve equations using the Addition and Multiplication Properties of Equations	22	(4)
Solve equations using the Distributive Property	26	(2)
Literal equations	28	(1)
Application problems	29	(7)
Value Mixture and Uniform Motion Problems	36	(7)
Value mixture problems	36	(2)
Uniform motion problems	38	(5)
Application Problems Involving Percent	43	(8)
Investment problems	43	(2)
Percent mixture problems	45	(6)
Inequalities in One Variable	51	(9)
Solve inequalities in one variable	51	(3)
Solve compound inequalities	54	(2)
Application problems	56	(4)
Absolute Value Equations and Inequalities	60	(17)
Absolute value equations	60	(4)
Absolute value inequalities	64	(2)
Application problems	66	(4)
Something Extra	70	(1)
Chapter Summary	71	(3)
Chapter Review Exercises	74	(3)
Linear Functions and Inequalities in Two variables	77	(82)
The Rectangular Coordinate System	79	(10)
Plot points in a rectangular coordinate system	79	(3)
Distance and midpoint formulas	82	(3)
Scatter diagrams	85	(4)
Introduction to Functions	89	(15)
Evaluate a function	89	(5)
Find the domain and range of a function	94	(3)
Determine whether or not a relation is a function	97	(7)
Linear Functions	104	(10)
Graph an equation of the form f(x) = mx + b or y = mx + b	104	(5)
Find the x- and y-intercepts of a straight line	109	(5)
Slope of a Straight Line	114	(11)
Find the slope of a line given two points	114	(2)
Graph a line given a point and the slope	116	(9)
Equations of Straight Lines and Their Inverses	125	(15)
Find the equation of a line given a point and the slope or given two points	125	(2)
Find the equations of parallel and perpendicular lines	127	(4)
Find the inverse of a linear function	131	(9)
Inequalities in Two Variables	140	(3)
Graph the solution set of an inequality in two variables	140	(3)
Applications of Linear Functions	143	(16)
Application problems	143	(8)
Something Extra	151	(1)
Chapter Summary	152	(2)
Chapter Review Exercises	154	(2)
Cumulative Review Exercises	156	(3)
Polynomials and Polynomial Functions	159	(74)
Exponential Expressions	161	(12)
Multiply monomials	161	(2)
Simplify expressions containing integer exponents	163	(4)
Scientific notation	167	(2)
Application problems	169	(4)
Introduction to Polynomials	173	(11)
Polynomial functions	173	(3)
Graphs and zeros of polynomial functions	176	(2)
Add and subtract polynomials	178	(6)
Multiplication of Polynomials	184	(9)
Multiply a polynomial by a monomial	184	(1)
Multiply polynomials	184	(4)
Application problems	188	(5)
Division of Polynomials	193	(8)
Divide polynomials	193	(2)
Synthetic division, the Remainder Theorem, and the Factor Theorem	195	(6)
Factoring Polynomials	201	(11)
Factor a monomial from a polynomial	201	(1)
Factor by grouping	202	(2)
Factor trinomials of the form x2 + bx + c	204	(2)
Factor trinomials of the form ax2 + bx + c	206	(6)
Special Factoring	212	(7)
Factor the difference of two perfect squares and perfect square trinomials	212	(1)
Factor the sum or the difference of two cubes	213	(2)
Factor trinomials that are quadratic in form	215	(1)
Factor completely	216	(3)
Solving Equations by Factoring	219	(14)
Solve equations by factoring	219	(3)
Application problems	222	(4)
Something Extra	226	(1)
Chapter Summary	227	(2)
Chapter Review Exercises	229	(1)
Cumulative Review Exercises	230	(3)
Rational Exponents and Radical Expressions	233	(46)
Rational Exponents and Radical Expressions	235	(11)
Simplify expressions with rational exponents	235	(2)
Write equivalent exponential and radical expressions	237	(2)
Simplify radical expressions	239	(7)
Operations on Radical Expressions	246	(7)
Add and subtract radical expressions	246	(1)
Multiply radical expressions	247	(1)
Divide radical expressions	248	(5)
Complex Numbers	253	(9)
Simplify complex numbers	253	(2)
Add and subtract complex numbers	255	(1)
Multiply and divide complex numbers	256	(6)
Radical Functions	262	(4)
Find the domain of a radical function	262	(1)
Graph a radical function	263	(3)
Equations Containing Radical Expressions	266	(13)
Solve equations containing radical expressions	266	(3)
Application problems	269	(4)
Something Extra	273	(1)
Chapter Summary	274	(1)
Chapter Review Exercises	275	(1)
Cumulative Review Exercises	276	(3)
Quadratic Functions and Inequalities	279	(48)
Solving Quadratic Equations by Factoring or by Taking Square Roots	281	(6)
Solve quadratic equations by factoring	281	(1)
Write a quadratic equation given its solutions	282	(1)
Solve quadratic equations by taking square roots	283	(4)
Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula	287	(9)
Solve quadratic equations by completing the square	287	(3)
Solve quadratic equations by using the quadratic formula	290	(6)
Equations That Are Reducible to Quadratic Equations	296	(7)
Equations that are quadratic in form	296	(2)
Radical equations	298	(1)
Fractional equations	299	(4)
Graphing Quadratic Functions	303	(11)
Graph a quadratic function	303	(5)
Find the x-intercepts of a parabola	308	(6)
Applications of Quadratic Equations	314	(4)
Minimum and maximum problems	314	(4)
Nonlinear Inequalities	318	(9)
Solve inequalities by factoring	318	(3)
Something Extra	321	(1)
Chapter Summary	322	(1)
Chapter Review Exercises	323	(2)
Cumulative Review Exercises	325	(2)
Rational Functions and Expressions	327	(56)
Introduction to Rational Functions	329	(7)
Find the domain of a rational function	329	(2)
Simplify rational expressions	331	(5)
Operations on Rational Expressions	336	(10)
Multiply and divide rational expressions	336	(2)
Add and subtract rational expressions	338	(8)
Complex Fractions	346	(6)
Simplify complex fractions	346	(6)
Rational Equations and Inequalities	352	(5)
Solve rational equations	352	(2)
Solve rational inequalities	354	(3)
Applications of Rational Equations	357	(10)
Work problems	357	(2)
Uniform motion problems	359	(8)
Proportions and Variation	367	(16)
Proportions	367	(1)
Variation	368	(8)
Something Extra	376	(1)
Chapter Summary	377	(1)
Chapter Review Exercises	378	(3)
Cumulative Review Exercises	381	(2)
Exponential and Logarithmic Functions	383	(52)
The Exponential Function	385	(8)
Evaluate exponential functions	385	(2)
Graph exponential functions	387	(6)
Introduction to Logarithms	393	(13)
Write equivalent exponential and logarithmic equations	393	(3)
The properties of logarithms	396	(10)
Graphs of Logarithmic Functions	406	(8)
Graph logarithmic functions	406	(8)
Exponential and Logarithmic Equations	414	(6)
Solve exponential equations	414	(2)
Solve logarithmic equations	416	(4)
Applications of Exponential and Logarithmic Functions	420	(15)
Application problems	420	(9)
Something Extra	429	(2)
Chapter Summary	431	(1)
Chapter Review Exercises	432	(1)
Cumulative Review Exercises	433	(2)
Conic Sections	435	(26)
The Parabola	437	(4)
Graph parabolas	437	(4)
The Circle	441	(5)
Graph circles	441	(5)
The Ellipse and the Hyperbola	446	(6)
Graph an ellipse with center at the origin	446	(2)
Graph a hyperbola with center at the origin	448	(4)
Quadratic Inequalities	452	(9)
Graph the solution set of a quadratic inequality in two variables	452	(2)
Something Extra	454	(2)
Chapter Summary	456	(1)
Chapter Review Exercises	457	(1)
Cumulative Review Exercises	458	(3)
Systems of Equations and Matrices	461	(60)
Solving Systems of Linear Equations by Graphing and by the Substitution Method	463	(8)
Solve systems of linear equations by graphing	463	(3)
Solve systems of linear equations by the substitution method	466	(5)
Solving Systems of Linear Equations by the Addition Method	471	(10)
Solve systems of two linear equations in two variables by the addition method	471	(3)
Solve systems of three linear equations in three variables by the addition method	474	(7)
Solving Nonlinear Systems of Equations and Systems of Inequalities	481	(8)
Solve nonlinear systems of equations	481	(5)
Graph the solution set of a system of inequalities	486	(3)
Solving Systems of Equations by using Matrices	489	(9)
Solve systems of equations by using matrices	489	(9)
Determinant of a Matrix	498	(8)
Evaluate determinants	498	(4)
Solve systems of equations by using Cramer's Rule	502	(4)
Application Problems in Two Variables	506	(15)
Rate-of-wind and water current problems	506	(2)
Application problems	508	(6)
Something Extra	514	(2)
Chapter Summary	516	(1)
Chapter Review Exercises	517	(2)
Cumulative Review Exercises	519	(2)
Sequences and Series	521	(29)
Introduction to Sequences and Series	523	(6)
Write the terms of a sequence	523	(2)
Find the sum of a series	525	(4)
Arithmetic Sequences and Series	529	(8)
Find the nth term of an arithmetic sequence	529	(3)
Find the sum of an arithmetic series	532	(1)
Application problems	533	(4)
Geometric Sequences and Series	537	(9)
Find the nth term of a geometric sequence	537	(2)
Finite geometric series	539	(1)
Infinite geometric series	540	(2)
Application problems	542	(4)
Binomial Expansions	546
Expand (a + b)n	546	(6)
Something Extra	552	(1)
Chapter Summary	553	(2)
Chapter Review Exercises	555	(1)
Cumulative Review Exercises	556
APPENDIX
Tips for Graphing	A3
Solutions to Problems	A11
Answers to Odd-Numbered Exercises	A65
Index