Algebra: Introductory and Intermediate, Fourth Edition

899 Pages·2006·31.35 MB·English

by  Richard N. Aufmann

Front_Matter_SE 11/7/05 9:19 AM Page i
Fourth Edition
Algebra: Introductory
and Intermediate
Richard N. Aufmann
Palomar College, California
Vernon C. Barker
Palomar College, California
Joanne S. Lockwood
New Hampshire Community Technical College
Houghton Mifflin Company
Boston New York
Front_Matter_SE 11/7/05 9:19 AM Page ii
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Instructor’s Annotated Edition:
ISBN 13: 978-0-618-61131-7
ISBN 10: 0-618-61131-2
For orders, use student text ISBNs:
ISBN 13: 978-0-618-60953-6
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Contents
Preface xi
AIM for Success xxiii
1 Real Numbers and Variable Expressions 1
Prep Test 2
Section 1.1 Integers 3
Objective A To use inequality symbols with integers 3
Objective B To find the additive inverse and absolute value of a number 4
Objective C To add or subtract integers 5
Objective D To multiply or divide integers 7
Objective E To solve application problems 10
Section 1.2 Rational and Irrational Numbers 17
Objective A To write a rational number as a decimal 17
Objective B To convert among percents, fractions, and decimals 18
Objective C To add or subtract rational numbers 19
Objective D To multiply or divide rational numbers 20
Objective E To evaluate exponential expressions 22
Objective F To simplify numerical radical expressions 24
Objective G To solve application problems 26
Section 1.3 The Order of Operations Agreement 33
Objective A To use the Order of Operations Agreement to simplify expressions 33
Section 1.4 Variable Expressions 37
Objective A To evaluate a variable expression 37
Objective B To simplify a variable expression using the Properties of Addition 38
Objective C To simplify a variable expression using the Properties of
Multiplication 40
Objective D To simplify a variable expression using the Distributive Property 42
Objective E To translate a verbal expression into a variable expression 44
Section 1.5 Sets 55
Objective A To write a set using the roster method 55
Objective B To write a set using set-builder notation 56
Objective C To graph an inequality on the number line 57
Focus on Problem Solving:Inductive Reasoning 61 • Projects and Group Activities:
Calculators 62• Chapter 1 Summary 63• Chapter 1 Review Exercises 67• Chapter 1
Test 69
2 First-Degree Equations and Inequalities 71
Prep Test 72
Section 2.1 Introduction to Equations 73
Objective A To determine whether a given number is a solution of an equation 73
Objective B To solve an equation of the form x (cid:2)a (cid:3)b 74
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Objective C To solve an equation of the form ax (cid:3) b 75
Objective D To solve application problems using the basic percent equation 77
Objective E To solve uniform motion problems 81
Section 2.2 General Equations 92
Objective A To solve an equation of the form ax (cid:2) b (cid:3) c 92
Objective B To solve an equation of the form ax (cid:2) b (cid:3) cx (cid:2) d 95
Objective C To solve an equation containing parentheses 97
Objective D To solve application problems using formulas 99
Section 2.3 Translating Sentences into Equations 106
Objective A To solve integer problems 106
Objective B To translate a sentence into an equation and solve 108
Section 2.4 Mixture and Uniform Motion Problems 113
Objective A To solve value mixture problems 113
Objective B To solve percent mixture problems 115
Objective C To solve uniform motion problems 117
Section 2.5 First-Degree Inequalities 125
Objective A To solve an inequality in one variable 125
Objective B To solve a compound inequality 128
Objective C To solve application problems 130
Section 2.6 Absolute Value Equations and Inequalities 137
Objective A To solve an absolute value equation 137
Objective B To solve an absolute value inequality 139
Objective C To solve application problems 141
Focus on Problem Solving: Trial-and-Error Approach to Problem Solving 147 • Projects
and Group Activities: Water Displacement 148 • Chapter 2 Summary 149 • Chapter 2
Review Exercises 152 • Chapter 2 Test 155 • Cumulative Review Exercises 157
3 Geometry 159
Prep Test 160
Section 3.1 Introduction to Geometry 161
Objective A To solve problems involving lines and angles 161
Objective B To solve problems involving angles formed by intersecting lines 166
Objective C To solve problems involving the angles of a triangle 169
Section 3.2 Plane Geometric Figures 177
Section 3.3 SOObbojjleeiccdttsiivv ee BA1 95TToo ssoollvvee pprroobblleemmss iinnvvoollvviinngg tthhee pareeraim oef tae rg oefo am geetroicm feigtruicre f ig18u2re 177 ghts reserved.
Objective A To solve problems involving the volume of a solid 195 y. All ri
Objective B To solve problems involving the surface area of a solid 198 an
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Focus on Problem Solving: More on the Trial-and-Error Approach to Problem Solving 205 • n C
Projects and Group Activities: Investigating Perimeter 206 • Symmetry 207 • Chapter 3 Miffli
Summary 207 • Chapter 3 Review Exercises 211 • Chapter 3 Test 213 • Cumulative n
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4 Linear Functions and Inequalities in
Two Variables 217
Prep Test 218
Section 4.1 The Rectangular Coordinate System 219
Objective A To graph points in a rectangular coordinate system 219
Objective B To determine ordered-pair solutions of an equation in two variables 221
Objective C To graph a scatter diagram 223
Section 4.2 Introduction to Functions 229
Objective A To evaluate a function 229
Section 4.3 Linear Functions 241
Objective A To graph a linear function 241
Objective B To graph an equation of the form Ax (cid:2)By (cid:3)C 243
Objective C To find the x- and y-intercepts of a straight line 246
Objective D To solve application problems 248
Section 4.4 Slope of a Straight Line 253
Objective A To find the slope of a line given two points 253
Objective B To graph a line given a point and the slope 257
Section 4.5 Finding Equations of Lines 264
Objective A To find the equation of a line given a point and the slope 264
Objective B To find the equation of a line given two points 265
Objective C To solve application problems 267
Section 4.6 Parallel and Perpendicular Lines 273
Objective A To find parallel and perpendicular lines 273
Section 4.7 Inequalities in Two Variables 279
Objective A To graph the solution set of an inequality in two variables 279
Focus on Problem Solving:Find a Pattern 283 • Projects and Group Activities:
Introduction to Graphing Calculators 284• Chapter 4 Summary 285• Chapter 4 Review
Exercises 288• Chapter 4 Test 291• Cumulative Review Exercises 293
5 Systems of Linear Equations and Inequalities 295
Prep Test 296
d. Section 5.1 Solving Systems of Linear Equations by Graphing and by the Substitution
hts reserve MObejetchtoivde A2T9o7 solve a system of linear equations by graphing 297
All rig OObbjjeeccttiivvee BC TToo ssoollvvee ain svyessttemme notf plirnoebaler meqsua3t0i3ons by the substitution method 300
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Section 5.4 Solving Systems of Linear Inequalities 329
Objective A To graph the solution set of a system of linear inequalities 329
Section 5.5 Solving Systems of Equations by Using Determinants (Available only online at this
textbook’s website at math.college.hmco.com/students. Under Developmental Mathematics, select course area,
then select textbook.)
Focus on Problem Solving:Solve an Easier Problem 333 • Projects and Group Activities:
Using a Graphing Calculator to Solve a System of Equations 333• Chapter 5 Summary
335• Chapter 5 Review Exercises 337• Chapter 5 Test 339• Cumulative Review
Exercises 341
6 Polynomials 343
Prep Test 344
Section 6.1 Exponential Expressions 345
Objective A To multiply monomials 345
Objective B To divide monomials and simplify expressions with negative
exponents 347
Objective C To write a number using scientific notation 351
Objective D To solve application problems 352
Section 6.2 Introduction to Polynomial Functions 357
Objective A To evaluate polynomial functions 357
Objective B To add or subtract polynomials 360
Section 6.3 Multiplication of Polynomials 365
Objective A To multiply a polynomial by a monomial 365
Objective B To multiply two polynomials 366
Objective C To multiply polynomials that have special products 368
Objective D To solve application problems 369
Section 6.4 Division of Polynomials 375
Objective A To divide a polynomial by a monomial 375
Objective B To divide polynomials 376
Objective C To divide polynomials by using synthetic division 378
Objective D To evaluate a polynomial function using synthetic division 380
Focus on Problem Solving:Dimensional Analysis 386 • Projects and Group Activities:
Astronomical Distances and Scientific Notation 388• Chapter 6 Summary 389• Chapter 6
Review Exercises 392• Chapter 6 Test 395• Cumulative Review Exercises 397
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Section 7.1 Common Factors 401 y.
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Objective B To factor by grouping 403 n
Section 7.2 Factoring Polynomials of the Form x2 (cid:2) bx (cid:2) c 407 n Miffli
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Objective A To factor a trinomial of the form x2(cid:2)bx (cid:2)c 407 ght
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Section 7.3 Factoring Polynomials of the Form ax2 (cid:2) bx (cid:2) c 415 ght
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Objective A To factor a trinomial of the form ax2(cid:2)bx (cid:2)c by using trial factors 415 op
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Objective B To factor a trinomial of the form ax2(cid:2)bx (cid:2)c by grouping 417
Section 7.4 Special Factoring 423
Objective A To factor the difference of two perfect squares or a perfect-square
trinomial 423
Objective B To factor the sum or difference of two perfect cubes 425
Objective C To factor a trinomial that is quadratic in form 426
Objective D To factor completely 427
Section 7.5 Solving Equations 433
Objective A To solve equations by factoring 433
Objective B To solve application problems 435
Focus on Problem Solving:Making a Table 441 • Projects and Group Activities:
Exploring Integers 442• Chapter 7 Summary 442• Chapter 7 Review Exercises 445•
Chapter 7 Test 447• Cumulative Review Exercises 449
8 Rational Expressions 451
Prep Test 452
Section 8.1 Multiplication and Division of Rational Expressions 453
Objective A To simplify a rational expression 453
Objective B To multiply rational expressions 454
Objective C To divide rational expressions 456
Section 8.2 Addition and Subtraction of Rational Expressions 461
Objective A To rewrite rational expressions in terms of a common denominator 461
Objective B To add or subtract rational expressions 463
Section 8.3 Complex Fractions 469
Objective A To simplify a complex fraction 469
Section 8.4 Solving Equations Containing Fractions 473
Objective A To solve an equation containing fractions 473
Section 8.5 Ratio and Proportion 477
Objective A To solve a proportion 477
Objective B To solve application problems 478
Objective C To solve problems involving similar triangles 478
Section 8.6 Literal Equations 485
Objective A To solve a literal equation for one of the variables 485
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9 Exponents and Radicals 515
Prep Test 516
Section 9.1 Rational Exponents and Radical Expressions 517
Objective A To simplify expressions with rational exponents 517
Objective B To write exponential expressions as radical expressions and to write
radical expressions as exponential expressions 519
Objective C To simplify radical expressions that are roots of perfect powers 521
Section 9.2 Operations on Radical Expressions 527
Objective A To simplify radical expressions 527
Objective B To add or subtract radical expressions 528
Objective C To multiply radical expressions 529
Objective D To divide radical expressions 531
Section 9.3 Solving Equations Containing Radical Expressions 537
Objective A To solve a radical equation 537
Objective B To solve application problems 539
Section 9.4 Complex Numbers 543
Objective A To simplify a complex number 543
Objective B To add or subtract complex numbers 544
Objective C To multiply complex numbers 545
Objective D To divide complex numbers 548
Focus on Problem Solving:Polya’s Four-Step Process 551 • Projects and Group
Activities:Solving Radical Equations with a Graphing Calculator 552• Chapter 9
Summary 553• Chapter 9 Review Exercises 555• Chapter 9 Test 557•
Cumulative Review Exercises 559
10 Quadratic Equations 561
Prep Test 562
Section 10.1 Solving Quadratic Equations by Factoring or by Taking Square Roots 563
Objective A To solve a quadratic equation by factoring 563
Objective B To write a quadratic equation given its solutions 564
Objective C To solve a quadratic equation by taking square roots 565
Section 10.2 Solving Quadratic Equations by Completing the Square 571
Objective A To solve a quadratic equation by completing the square 571
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Section 10.4 Solving Equations That Are Reducible to Quadratic Equations 583 All rig
Objective A To solve an equation that is quadratic in form 583 y.
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Section 10.5 Quadratic Inequalities and Rational Inequalities 589 on
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Section 10.6 Applications of Quadratic Equations 593 ht
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Objective A To solve application problems 593 pyri
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Focus on Problem Solving:Using a Variety of Problem-Solving Techniques 597 • Projects
and Group Activities:Using a Graphing Calculator to Solve a Quadratic Equation 597•
Chapter 10 Summary 598• Chapter 10 Review Exercises 601• Chapter 10 Test 603•
Cumulative Review Exercises 605
11 Functions and Relations 607
Prep Test 608
Section 11.1 Properties of Quadratic Functions 609
Objective A To graph a quadratic function 609
Objective B To find the x-intercepts of a parabola 612
Objective C To find the minimum or maximum of a quadratic function 615
Objective D To solve application problems 616
Section 11.2 Graphs of Functions 625
Objective A To graph functions 625
Section 11.3 Algebra of Functions 631
Objective A To perform operations on functions 631
Objective B To find the composition of two functions 633
Section 11.4 One-to-One and Inverse Functions 639
Objective A To determine whether a function is one-to-one 639
Objective B To find the inverse of a function 640
Section 11.5 Conic Sections (Available only online at this textbook’s website at math.college.hmco.com/students.
Under Developmental Mathematics, select course area, then select textbook.)
Focus on Problem Solving:Algebraic Manipulation and Graphing Techniques 647 •
Projects and Group Activities:Finding the Maximum or Minimum of aFunction Using a
Graphing Calculator 648• Business Applications of Maximum and Minimum Values of
Quadratic Functions 648• Chapter 11 Summary 650• Chapter 11 Review Exercises 653•
Chapter 11 Test 655• Cumulative Review Exercises 657
12 Exponential and Logarithmic Functions 659
Prep Test 660
Section 12.1 Exponential Functions 661
Objective A To evaluate an exponential function 661
Objective B To graph an exponential function 663
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