Intermediate Alegbra With Applications

by Unknown

• ISBN13: 9780395969618
• ISBN10: 0395969611
• Edition: 5th
• Format: Paperback
• Copyright: 1999-07-16
• Publisher: Brooks Cole

Table of Contents

Preface	xiii
Index of Applications	xxv
Review of Real Numbers	1	(52)
Introduction to Real Numbers	3	(12)
Inequality and absolute value	3	(3)
Set operations and interval notation	6	(9)
Operations on Rational Numbers	15	(13)
Operations on integers	15	(3)
Operations on rational numbers	18	(3)
Exponential expressions	21	(1)
The Order of Operations Agreement	22	(6)
Variable Expressions	28	(9)
The Properties of the Real Numbers	28	(2)
Evaluate variable expressions	30	(2)
Simplify variable expressions	32	(5)
Verbal Expressions and Variable Expressions	37	(16)
Translate a verbal expression into a variable expression	37	(2)
Application problems	39	(4)
Focus on Problem Solving: Polya's Four-Step Process	43	(3)
Projects and Group Activities: Water Displacement	46	(1)
Chapter Summary	47	(2)
Chapter Review Exercises	49	(1)
Chapter Test	50	(3)
First-Degree Equations and Inequalities	53	(64)
Equations in One Variable	55	(10)
Solve equations using the Addition and Multiplication Properties of Equations	55	(3)
Solve equations using the Distributive Property	58	(2)
Application problems	60	(5)
Coin, Stamp, and Integer Problems	65	(7)
Coin and stamp problems	65	(2)
Integer problems	67	(5)
Value Mixture and Motion Problems	72	(7)
Value mixture problems	72	(1)
Uniform motion problems	73	(6)
Applications: Problems Involving Percent	79	(9)
Investment problems	79	(2)
Percent mixture problems	81	(7)
Inequalities in One Variable	88	(10)
Solve inequalities in one variable	88	(2)
Solve compound inequalities	90	(2)
Application problems	92	(6)
Absolute Value Equations and Inequalities	98	(19)
Absolute value equations	98	(2)
Absolute value inequalities	100	(2)
Application problems	102	(4)
Focus on Problem Solving: Understand the Problem	106	(1)
Projects and Group Activities: Venn Diagrams	107	(1)
Absolute Value Equations and Inequalities	108	(1)
Chapter Summary	109	(3)
Chapter Review Exercises	112	(1)
Chapter Test	113	(1)
Cumulative Review Exercises	114	(3)
Linear Functions and Inequalities in Two Variables	117	(76)
The Rectangular Coordinate System	119	(10)
Points on a rectangular coordinate system	119	(2)
Find the length and midpoint of a line segment	121	(2)
Graph a scatter diagram	123	(6)
Introduction to Functions	129	(13)
Evaluate a function	129	(13)
Linear Functions	142	(13)
Graph a linear function	142	(2)
Graph an equation of the form Ax + By = C	144	(5)
Application problems	149	(6)
Slope of a Straight Line	155	(9)
Find the slope of a line given two points	155	(3)
Graph a line given a point and the slope	158	(6)
Finding Equations of Lines	164	(8)
Find the equation of a line given a point and the slope	164	(2)
Find the equation of a line given two points	166	(1)
Application problems	167	(5)
Parallel and Perpendicular Lines	172	(7)
Find equations of parallel and perpendicular lines	172	(7)
Inequalities in Two Variables	179	(14)
Graph the solution set of an inequality in two variables	179	(3)
Focus on Problem Solving: Find a Pattern	182	(2)
Projects and Group Activities: Evaluating a Function with a Graphing Calculator	184	(1)
Introduction to Graphing Calculators	184	(1)
Chapter Summary	185	(2)
Chapter Review Exercises	187	(3)
Chapter Test	190	(1)
Cumulative Review Exercises	191	(2)
Systems of Equations and Inequalities	193	(58)
Solving Systems of Linear Equations by Graphing and by the Substitution Method	195	(7)
Solve a system of linear equations by graphing	195	(2)
Solve a system of linear equations by the substitution method	197	(5)
Solving Systems of Linear Equations by the Addition Method	202	(10)
Solve a system of two linear equations in two variables by the addition method	202	(2)
Solve a system of three linear equations in three variables by the addition method	204	(8)
Solving Systems of Equations by Using Determinants and by Using Matrices	212	(13)
Evaluate determinants	212	(2)
Solve systems of linear equations by using Cramer's Rule	214	(3)
Solve systems of linear equations by using matrices	217	(8)
Application Problems	225	(11)
Rate-of-wind and water-current problems	225	(2)
Application problems	227	(9)
Solving Systems of Linear Inequalities	236	(15)
Graph the solution set of a system of linear inequalities	236	(3)
Focus on Problem Solving: Solve an Easier Problem	239	(1)
Projects and Group Activities: Using a Graphing Calculator to Solve a System of Equations	240	(1)
Solving a First-Degree Equation with a Graphing Calculator	241	(2)
Chapter Summary	243	(3)
Chapter Review Exercises	246	(1)
Chapter Test	247	(2)
Cumulative Review Exercises	249	(2)
Polynomials and Exponents	251	(74)
Exponential Expressions	253	(11)
Multiply monomials	253	(1)
Divide monomials and simplify expressions with negative exponents	254	(4)
Scientific notation	258	(1)
Application problems	259	(5)
Introduction to Polynomials	264	(10)
Evaluate polynomial functions	264	(4)
Add or subtract polynomials	268	(6)
Multiplication of Polynomials	274	(8)
Multiply a polynomial by a monomial	274	(1)
Multiply to polynomials	275	(1)
Multiply polynomials that have special products	276	(1)
Application problems	277	(5)
Division of Polynomials	282	(7)
Divide polynomials	282	(1)
Synthetic division	283	(2)
Evaluate a polynomial using synthetic division	285	(4)
Factoring Polynomials	289	(11)
Factor a monomial from a polynomial	289	(1)
Factor by grouping	290	(1)
Factor trinomials of the form x2 + bx + c	291	(2)
Factor trinomials of the form ax2 + bx + c	293	(7)
Special Factoring	300	(8)
Factor the difference of two perfect squares and factor perfect-square trinomials	300	(2)
Factor the sum or the difference of two cubes	302	(1)
Factor trinomials that are quadratic in form	303	(1)
Factor completely	304	(4)
Solving Equations by Factoring	308	(17)
Solve equations by factoring	308	(2)
Application problems	310	(5)
Focus on Problem Solving: Find a Counterexample	315	(1)
Projects and Group Activities: Reverse Polish Notation	316	(1)
Pythagorean Triples	317	(1)
Chapter Summary	318	(2)
Chapter Review Exercises	320	(2)
Chapter Test	322	(1)
Cumulative Review Exercises	323	(2)
Rational Expressions	325	(52)
Introduction to Rational Functions	327	(6)
Find the domain of a rational function	327	(2)
Simplify rational expressions	329	(4)
Operations on Rational Expressions	333	(8)
Multiply and divide rational expressions	333	(1)
Add and subtract rational expressions	334	(7)
Complex Fractions	341	(4)
Simplify complex fractions	341	(4)
Rational Equations	345	(10)
Solve fractional equations	345	(1)
Work problems	346	(2)
Uniform motion problems	348	(7)
Proportions and Variation	355	(10)
Proportions	355	(2)
Variation problems	357	(8)
Literal Equations	365	(12)
Solve literal equations	365	(2)
Focus on Problem Solving: Implication	367	(1)
Projects and Group Activities: Continued Fractions	368	(1)
Graphing Rational Expressions	369	(1)
Chapter Summary	370	(2)
Chapter Review Exercises	372	(2)
Chapter Test	374	(1)
Cumulative Review Exercises	375	(2)
Rational Exponents and Radicals	377	(52)
Rational Exponents and Radical Expressions	379	(8)
Simplify expressions with rational exponents	379	(2)
Write exponential expressions as radical expressions and radical expressions as exponential expressions	381	(1)
Simplify radical expressions that are roots of perfect powers	382	(5)
Operations on Radical Expressions	387	(9)
Simplify radical expressions	387	(1)
Add and subtract radical expressions	388	(1)
Multiply radical expressions	389	(1)
Divide radical expressions	390	(6)
Complex Numbers	396	(8)
Simplify complex numbers	396	(2)
Add and subtract complex numbers	398	(1)
Multiply complex numbers	398	(2)
Divide complex numbers	400	(4)
Radical Functions	404	(6)
Find the domain of a radical function	404	(1)
Graph a radical function	405	(5)
Solving Equations Containing Radical Expressions	410	(19)
Solve equations containing one or more radical expressions	410	(2)
Application problems	412	(6)
Focus on Problem Solving: Another Look at Polya's Four-Step Process	418	(1)
Projects and Group Activities: Graphing Complex Numbers	419	(2)
Solving Radical Equations with a Graphing Calculator	421	(1)
Chapter Summary	422	(1)
Chapter Review Exercises	423	(2)
Chapter Test	425	(1)
Cumulative Review Exercises	426	(3)
Quadratic Equations and Inequalities	429	(66)
Solving Quadratic Equations by Factoring or by Taking Square Roots	431	(7)
Solve quadratic equations by factoring	431	(1)
Write a quadratic equation given its solutions	432	(1)
Solve quadratic equations by taking square roots	433	(5)
Solving Quadratic Equations by Completing the Square and by Using the Quadratic Formula	438	(11)
Solve quadratic equations by completing the square	438	(3)
Solve quadratic equations by using the quadratic formula	441	(8)
Equations That Are Reducible to Quadratic Equations	449	(7)
Equations that are quadratic in form	449	(2)
Radical equations	451	(1)
Fractional equations	452	(4)
Applications of Quadratic Equations	456	(6)
Application problems	456	(6)
Nonlinear Inequalities	462	(4)
Solve inequalities by factoring	462	(1)
Solve rational inequalities	463	(3)
Properties of Quadratic Functions	466	(13)
Graph a quadratic function	466	(4)
Find the x-intercepts of a parabola	470	(9)
Applications of Quadratic Functions	479	(16)
Minimum and maximum problems	479	(1)
Applications of minimum and maximum	480	(4)
Focus on Problem Solving: Inductive and Deductive Reasoning	484	(1)
Projects and Group Activities: Completing the Square	485	(1)
Using a Graphing Calculator to Solve a Quadratic Equation	486	(1)
Solving Nonlinear Inequalities Using a Graphing Calculator	487	(1)
Chapter Summary	488	(2)
Chapter Review Exercises	490	(1)
Chapter Test	491	(1)
Cumulative Review Exercises	492	(3)
Functions and Relations	495	(44)
Graphs of Functions	497	(9)
Graph functions	497	(9)
Translations of Graphs	506	(7)
Graph by using translations	506	(7)
Algebra of Functions	513	(5)
Perform operations on functions	513	(2)
Find the composition of two functions	515	(3)
One-to-One and Inverse Functions	518	(21)
Determine whether a function is one-to-one	518	(2)
Find the inverse of a function	520	(7)
Focus on Problem Solving: Proof in Mathematics	527	(1)
Projects and Group Activities: Derivative Investments	528	(2)
Properties of Polynomials	530	(1)
The Greatest-Integer Function	531	(1)
Chapter Summary	532	(2)
Chapter Review Exercises	534	(2)
Chapter Test	536	(1)
Cumulative Review Exercises	537	(2)
Exponential and Logarithmic Functions	539	(58)
Exponential Functions	541	(9)
Evaluate exponential functions	541	(2)
Graph exponential functions	543	(7)
Introduction to Logarithms	550	(13)
Write equivalent exponential and logarithmic equations	550	(3)
The Properties of Logarithms	553	(10)
Graphs of Logarithmic Functions	563	(7)
Graph logarithmic functions	563	(7)
Exponential and Logarithmic Equations	570	(8)
Solve exponential equations	570	(2)
Solve logarithmic equations	572	(6)
Applications of Exponential and Logarithmic Functions	578	(19)
Application problems	578	(10)
Focus on Problem Solving: Proof by Contradiction	588	(1)
Projects and Group Activities: Fractals	589	(2)
Chapter Summary	591	(1)
Chapter Review Exercises	592	(1)
Chapter Test	593	(1)
Cumulative Review Exercises	594	(3)
Sequences and Series	597	(40)
Introduction to Sequences and Series	599	(6)
Write the terms of a sequence	599	(1)
Find the sum of a series	600	(5)
Arithmetic Sequences and Series	605	(7)
Find the nth term of an arithmetic sequence	605	(2)
Find the sum of an arithmetic series	607	(1)
Application problems	608	(4)
Geometric Sequences and Series	612	(9)
Find the nth term of a geometric sequence	612	(1)
Finite geometric series	613	(2)
Infinite geometric series	615	(2)
Application problems	617	(4)
Binomial Expansions	621	(16)
Expand (a + n)n	621	(6)
Focus on Problem Solving: Forming Negations	627	(1)
Projects and Group Activities: ISBN and UPC Numbers	628	(1)
Finding the Proper Dosage	629	(2)
Chapter Summary	631	(1)
Chapter Review Exercises	632	(2)
Chapter Test	634	(1)
Cumulative Review Exercises	635	(2)
Conic Sections	637	(38)
The Parabola	639	(5)
Graph parabolas	639	(5)
The Circle	644	(6)
Find the equation of a circle and then graph the circle	644	(2)
Write the equation of a circle in standard form and then graph the circle	646	(4)
The Ellipse and the Hyperbola	650	(7)
Graph an ellipse with center at the origin	650	(2)
Graph a hyperbola with center at the origin	652	(5)
Solving Nonlinear Systems of Equations	657	(5)
Solve nonlinear systems of equations	657	(5)
Quadratic Inequalities and Systems of Inequalities	662	(13)
Graph the solution set of a quadratic inequality in two variables	662	(1)
Graph the solution set of a nonlinear system of inequalities	663	(5)
Focus on Problem Solving: Use a Variety of Problem-Solving Strategies	668	(1)
Projects and Group Activities: Graphing Conic Sections Using a Graphing Utility	668	(1)
Chapter Summary	669	(2)
Chapter Review Exercises	671	(2)
Chapter Test	673	(2)
Final Exam	675	(4)
Appendix: Guidelines for Using Graphing Calculators	679
Solutions to Problems	S1
Answers to Odd-Numbered Exercises	A1
Glossary	G1
Index	I1