Precalculus Graphs & Models

Cover......Page 1
Title Page......Page 3
Copyright......Page 4
ISBN-13: 9780073519531......Page 6
Preface......Page 8
Contents......Page 30
Index of Applications......Page 37
CHAPTER 1 Relations, Functions, and Graphs......Page 49
A. Relations, Mapping Notation, and Ordered Pairs......Page 50
B. The Graph of a Relation......Page 51
C. Graphing Relations on a Calculator......Page 54
D. The Equation and Graph of a Circle......Page 56
A. The Graph of a Linear Equation......Page 67
B. The Slope of a Line and Rates of Change......Page 68
C. Horizontal Lines and Vertical Lines......Page 71
D. Parallel and Perpendicular Lines......Page 73
E. Applications of Linear Equations......Page 75
A. Functions and Relations......Page 81
B. The Domain and Range of a Function......Page 84
C. Function Notation......Page 87
D. Reading and Interpreting Information Given Graphically......Page 89
Reinforcing Basic Concepts: Finding the Domain and Range of a Relation from Its Graph......Page 96
A. Linear Equations, Slope-Intercept Form and Function Form......Page 98
B. Slope-Intercept Form and the Graph of a Line......Page 100
C. Linear Equations in Point-Slope Form......Page 103
D. Applications of Linear Equations......Page 104
A. Solving Equations Graphically Using the Intersect Method......Page 112
B. Solving Equations Graphically Using the x-Intercept/Zeroes Method......Page 114
C. Solving Linear Inequalities Graphically......Page 116
D. Solving for a Specified Variable in Literal Equations......Page 117
E. Using a Problem-Solving Guide......Page 119
A. Scatterplots and Positive/Negative Associations......Page 127
B. Scatterplots and Linear/Nonlinear Associations......Page 128
C. Identifying Strong and Weak Correlations......Page 129
D. Linear Functions That Model Relationships Observed in a Set of Data......Page 131
E. Linear Regression and the Line of Best Fit......Page 133
Making Connections......Page 141
Summary and Concept Review......Page 142
Practice Test......Page 147
Strengthening Core Skills: The Various Forms of a Linear Equation......Page 148
Calculator Exploration and Discovery: Evaluating Expressions and Looking for Patterns......Page 149
Connections to Calculus: Tangent Lines......Page 151
CHAPTER 2 More on Functions......Page 153
A. Graphs and Symmetry......Page 154
B. Intervals Where a Function Is Positive or Negative......Page 156
C. Intervals Where a Function Is Increasing or Decreasing......Page 158
E. Locating Maximum and Minimum Values Using Technology......Page 160
A. The Toolbox Functions......Page 168
B. Vertical and Horizontal Shifts......Page 170
C. Vertical and Horizontal Reflections......Page 172
D. Vertically Stretching/Compressing a Basic Graph......Page 174
E. Transformations of a General Function......Page 175
A. Solving Absolute Value Equations......Page 184
B. Solving “Less Than” Absolute Value Inequalities......Page 187
C. Solving “Greater Than” Absolute Value Inequalities......Page 188
E. Applications Involving Absolute Value......Page 190
Mid-Chapter Check......Page 194
Reinforcing Basic Concepts: Using Distance to Understand Absolute Value Equations and Inequalities......Page 195
A. Rational Functions and Asymptotes......Page 196
B. Using Asymptotes to Graph Basic Rational Functions......Page 199
C. Graphs of Basic Power Functions......Page 200
D. Applications of Rational and Power Functions......Page 203
2.5 Piecewise-Defined Functions......Page 211
A. The Domain of a Piecewise-Defined Function......Page 212
B. Graphing Piecewise-Defined Functions......Page 213
C. Applications of Piecewise-Defined Functions......Page 218
A. Toolbox Functions and Direct Variation......Page 225
B. Inverse Variation......Page 228
C. Joint or Combined Variations......Page 230
Making Connections......Page 236
Summary and Concept Review......Page 237
Practice Test......Page 241
Calculator Exploration and Discovery: Studying Joint Variations......Page 243
Strengthening Core Skills: Variation and Power Functions: y = kxᴾ......Page 244
Cumulative Review: Chapters 1–2......Page 245
Connections to Calculus: Solving Various Types of Equations; Absolute Value Inequalities and Delta/Epsilon Form......Page 247
CHAPTER 3 Quadratic Functions and Operations on Functions......Page 251
A. Identifying and Simplifying Imaginary and Complex Numbers......Page 252
B. Adding and Subtracting Complex Numbers......Page 254
C. Multiplying Complex Numbers; Powers of i......Page 255
A. Zeroes of Quadratic Functions and x-Intercepts of Quadratic Graphs......Page 262
B. Quadratic Equations and the Square Root Property of Equality......Page 265
C. Solving Quadratic Equations by Completing the Square......Page 267
D. The Quadratic Formula and the Discriminant......Page 269
E. Quadratic Inequalities......Page 273
F. Applications of Quadratic Functions and Inequalities......Page 276
A. Graphing Quadratic Functions by Completing the Square......Page 283
B. Graphing Quadratic Functions Using the Vertex Formula......Page 285
D. Quadratic Functions and Extreme Values......Page 286
Reinforcing Basic Concepts: An Alternative Method for Checking Solutions to Quadratic Equations......Page 297
A. Quadratic Equation Models......Page 298
B. Nonlinear Functions and Rates of Change......Page 301
C. The Average Rate of Change Formula......Page 302
A. Sums and Differences of Functions......Page 310
B. Products and Quotients of Functions......Page 311
C. Graphical and Numerical Views of Operations on Functions......Page 313
D. Applications of the Algebra of Functions......Page 315
A. The Composition of Functions......Page 322
B. A Numerical and Graphical View of the Composition of Functions......Page 327
C. Average Rates of Change and the Difference Quotient......Page 329
D. Applications of Composition and the Difference Quotient......Page 332
Summary and Concept Review......Page 340
Practice Test......Page 345
Calculator Exploration and Discovery: Residuals, Correlation Coefficients, and Goodness of Fit......Page 346
Strengthening Core Skills: Base Functions and Quadratic Graphs......Page 348
Cumulative Review: Chapters 1–3......Page 349
Connections to Calculus: Rates of Change and the Difference Quotient; Transformations and the Area Under a Curve......Page 351
CHAPTER 4 Polynomial and Rational Functions......Page 355
A. Long Division and Synthetic Division......Page 356
B. The Remainder Theorem......Page 360
C. The Factor Theorem......Page 361
D. Applications......Page 363
A. The Fundamental Theorem of Algebra......Page 368
B. Real Polynomials and the Intermediate Value Theorem......Page 371
C. The Rational Zeroes Theorem......Page 373
D. Descartes’ Rule of Signs and Upper/Lower Bounds......Page 376
E. Applications of Polynomial Functions......Page 379
A. Identifying the Graph of a Polynomial Function......Page 385
B. The End-Behavior of a Polynomial Graph......Page 386
C. Attributes of Polynomial Graphs with Zeroes of Multiplicity......Page 389
D. The Graph of a Polynomial Function......Page 393
E. Applications of Polynomials and Polynomial Modeling......Page 395
Mid-Chapter Check......Page 402
Reinforcing Basic Concepts: Approximating Real Zeroes......Page 403
A. Rational Functions and Vertical Asymptotes......Page 404
B. Vertical Asymptotes and Multiplicities......Page 406
C. Finding Horizontal Asymptotes......Page 407
D. The Graph of a Rational Function......Page 409
E. Applications of Rational Functions......Page 413
4.5 Additional Insights into Rational Functions......Page 419
A. Rational Functions and Removable Discontinuities......Page 420
B. Rational Functions with Oblique or Nonlinear Asymptotes......Page 422
C. Applications of Rational Functions......Page 425
A. Polynomial Inequalities......Page 433
B. Rational Inequalities......Page 436
C. Applications of Inequalities......Page 438
Summary and Concept Review......Page 444
Practice Test......Page 448
Calculator Exploration and Discovery: Complex Zeroes, Repeated Zeroes, and Inequalities......Page 449
Strengthening Core Skills: Solving Inequalities Using the Push Principle......Page 450
Cumulative Review: Chapters 1–4......Page 451
Connections to Calculus: Graphing Techniques......Page 453
CHAPTER 5 Exponential and Logarithmic Functions......Page 457
A. Identifying One-to-One Functions......Page 458
B. Inverse Functions and Ordered Pairs......Page 459
C. Finding Inverse Functions Using an Algebraic Method......Page 460
D. The Graph of a Function and Its Inverse......Page 463
E. Applications of Inverse Functions......Page 465
A. Evaluating Exponential Functions......Page 470
B. Graphing Exponential Functions......Page 471
C. The Base-e Exponential Function: f(x) = eˣ......Page 473
D. Solving Exponential Equations Using the Uniqueness Property......Page 474
A. Exponential Equations and Logarithmic Form......Page 481
B. Finding Common Logarithms and Natural Logarithms......Page 483
C. Graphing Logarithmic Functions......Page 484
D. Finding the Domain of a Logarithmic Function......Page 485
E. Applications of Logarithms......Page 486
A. Solving Equations Using the Fundamental Properties of Logarithms......Page 494
B. The Product, Quotient, and Power Properties of Logarithms......Page 497
D. Solving Applications of Logarithms......Page 500
Mid-Chapter Check......Page 504
A. Solving Logarithmic and Exponential Equations......Page 505
B. Applications of Logistic, Exponential, and Logarithmic Functions......Page 511
A. Simple and Compound Interest......Page 517
B. Interest Compounded Continuously......Page 519
C. Applications Involving Annuities and Amortization......Page 520
D. Applications Involving Exponential Growth and Decay......Page 523
A. Choosing an Appropriate Form of Regression......Page 530
B. Exponential and Logarithmic Regression Models......Page 531
C. Logistic Equations and Regression Models......Page 533
D. Applications of Regression......Page 534
Making Connections......Page 543
Summary and Concept Review......Page 544
Practice Test......Page 549
Calculator Exploration and Discovery: Investigating Logistic Equations......Page 550
Strengthening Core Skills: The HerdBurn Scale—What’s Hot and What’s Not......Page 551
Cumulative Review: Chapters 1–5......Page 552
Connections to Calculus: Properties of Logarithms; Area Functions; Expressions Involving eˣ......Page 553
CHAPTER 6 An Introduction to Trigonometric Functions......Page 557
A. Angle Measure in Degrees......Page 558
B. Triangles and Properties of Triangles......Page 560
C. Angle Measure in Radians; Arc Length and Area......Page 562
D. Converting Between Degrees and Radians......Page 565
E. Angular and Linear Velocity......Page 568
A. The Unit Circle......Page 575
B. Special Triangles and the Unit Circle......Page 577
C. Trigonometric Functions and Points on the Unit Circle......Page 580
D. The Trigonometry of Real Numbers......Page 582
E. Finding a Real Number t Whose Function Value Is Known......Page 584
A. Graphing f(t) = sin t......Page 590
B. Graphing f(t) = cos t......Page 597
C. Graphing y = A sin(Bt) and y = A cos(Bt)......Page 599
D. Writing Equations from Graphs......Page 602
A. Graphs of y = A csc(Bt) and y = A sec(Bt)......Page 609
B. The Graph of y = tan t......Page 611
C. The Graph of y = cot t......Page 614
D. Characteristics of y = tan t and y = cot t......Page 615
E. Graphing y = A tan(Bt) and y = A cot(Bt)......Page 616
Reinforcing Basic Concepts: Trigonometry of the Real Numbers and the Wrapping Function......Page 625
A. Vertical Translations: y = A sin(Bt) + D and y = A cos(Bt) + D......Page 626
B. Horizontal Translations: y = A sin(Bt + C) + D and y = A cos(Bt + C) + D......Page 629
C. Simple Harmonic Motion: y = A sin(Bt) or y = A cos(Bt)......Page 632
D. Vertical and Horizontal Translations of Other Trig Functions......Page 634
E. Applications of the Remaining Trig Functions......Page 636
A. Trigonometric Ratios and Their Values......Page 643
B. Solving Right Triangles Given One Angle and One Side......Page 645
C. Solving Right Triangles Given Two Sides......Page 647
D. Using Cofunctions and Complements to Write Equivalent Expressions......Page 648
E. Applications of Right Triangles......Page 649
A. Trigonometric Ratios and the Point P(x, y)......Page 658
B. Reference Angles and the Trig Functions of Any Angle......Page 662
C. Applications of the Trig Functions of Any Angle......Page 665
A. Critical Points and Sinusoidal Models......Page 670
B. Data and Sinusoidal Regression......Page 674
Making Connections......Page 681
Summary and Concept Review......Page 682
Practice Test......Page 691
Calculator Exploration and Discovery: Variable Amplitudes and Modeling the Tides......Page 693
Strengthening Core Skills: Standard Angles, Reference Angles, and the Trig Functions......Page 694
Cumulative Review: Chapters 1–6......Page 696
Connections to Calculus: Right Triangle Relationships; Converting from Rectangular Coordinates to Trigonometric (Polar) Form......Page 698
CHAPTER 7 Trigonometric Identities, Inverses, and Equations......Page 701
A. Fundamental Identities and Identity Families......Page 702
B. Verifying an Identity Using Algebra......Page 703
C. Writing One Function in Terms of Another......Page 705
A. Identities Due to Symmetry......Page 709
B. Verifying Identities......Page 710
C. Showing an Equation Is Not an Identity......Page 713
A. The Sum and Difference Identities for Cosine......Page 717
B. The Sum and Difference Identities for Sine and Tangent......Page 720
C. Verifying Other Identities......Page 722
A. The Double-Angle Identities......Page 728
B. The Power Reduction and Half-Angle Identities......Page 730
C. The Product-to-Sum Identities......Page 733
D. Applications of Identities......Page 734
Reinforcing Basic Concepts: Identities—Connections and Relationships......Page 741
A. The Inverse Sine Function......Page 743
B. The Inverse Cosine and Inverse Tangent Functions......Page 746
C. Using the Inverse Trig Functions to Evaluate Compositions......Page 748
D. The Inverse Functions for Secant, Cosecant, and Cotangent......Page 750
E. Applications of Inverse Trig Functions......Page 752
A. The Principal Root, Roots in [0, 2π), and Real Roots......Page 759
C. Solving Trig Equations for Roots in [0,2π) or [0°, 360°)......Page 760
D. Solving Trig Equations for All Real Roots (R)......Page 762
A. Trig Equations and Algebraic Methods......Page 769
C. Trig Equations and Graphing Technology......Page 771
D. Solving Equations of the Form Asin (Bx ± C) ±; D = k......Page 773
E. Applications Using Trigonometric Equations......Page 774
Making Connections......Page 780
Summary and Concept Review......Page 781
Practice Test......Page 785
Strengthening Core Skills: Trigonometric Equations and Inequalities......Page 787
Cumulative Review: Chapters 1–7......Page 789
Connections to Calculus: Simplifying Expressions Using a Trigonometric Substitution; Trigonometric Identities and Equations......Page 791
CHAPTER 8 Applications of Trigonometry......Page 793
A. The Law of Sines and Unique Solutions......Page 794
B. Solving SSA Triangles—The Ambiguous Case......Page 796
C. Applications of the Law of Sines......Page 800
A. The Law of Cosines and SAS Triangles......Page 807
B. The Law of Cosines and SSS Triangles......Page 809
C. Applications Using the Law of Cosines......Page 810
D. Trigonometry and the Area of a Triangle......Page 811
A. The Notation and Geometry of Vectors......Page 819
B. Vectors and the Rectangular Coordinate System......Page 820
C. Operations on Vectors and Vector Properties......Page 824
D. Algebraic Vectors, Unit Vectors, and i, j Form......Page 826
E. Vector Diagrams and Vector Applications......Page 827
Reinforcing Basic Concepts: Scaled Drawings and the Laws of Sine and Cosine......Page 834
A. Vectors and Equilibrium......Page 835
B. The Component of u along v: comp[Sub(v)]u......Page 836
C. Vector Applications Involving Work......Page 838
D. Dot Products and the Angle Between Two Vectors......Page 840
E. Vector Projections and Orthogonal Components......Page 842
A. Graphing Complex Numbers......Page 850
B. Complex Numbers in Trigonometric Form......Page 851
C. Converting from Trigonometric Form to Rectangular Form......Page 852
D. Interpreting Products and Quotients Geometrically......Page 853
E. Products and Quotients in Trigonometric Form......Page 854
F. (Optional) Applications of Complex Numbers......Page 855
A. De Moivre’s Theorem......Page 861
B. Checking Solutions to Polynomial Equations......Page 862
C. The nth Roots Theorem......Page 863
Making Connections......Page 869
Summary and Concept Review......Page 870
Practice Test......Page 874
Strengthening Core Skills: Vectors and Static Equilibrium......Page 876
Cumulative Review: Chapters 1–8......Page 877
Connections to Calculus: Trigonometry and Problem Solving; Vectors in Three Dimensions......Page 880
CHAPTER 9 Systems of Equations and Inequalities......Page 885
A. Solutions to a System of Equations......Page 886
B. Solving Systems Graphically......Page 887
C. Solving Systems by Substitution......Page 888
D. Solving Systems Using Elimination......Page 889
E. Inconsistent and Dependent Systems......Page 891
F. Systems and Modeling......Page 892
A. Visualizing Solutions in Three Dimensions......Page 901
B. Solutions to a System of Three Equations in Three Variables......Page 902
C. Solving Systems of Three Equations in Three Variables Using Elimination......Page 903
D. Inconsistent and Dependent Systems......Page 906
E. Applications......Page 908
A. Linear Inequalities in Two Variables......Page 913
B. Solving Systems of Linear Inequalities......Page 915
C. Applications of Systems of Linear Inequalities......Page 917
D. Linear Programming......Page 918
A. Setting Up a Decomposition Template......Page 927
B. Decomposition Using Convenient Values......Page 930
C. Decomposition Using a System of Equations......Page 933
D. Partial Fractions and Telescoping Sums......Page 934
Mid-Chapter Check......Page 939
Reinforcing Basic Concepts: Window Size and Graphing Technology......Page 940
B. The Augmented Matrix of a System of Equations......Page 941
C. Solving a System Using Matrices......Page 943
D. Solving Systems of Equations Using Technology......Page 946
E. Inconsistent and Dependent Systems......Page 947
F. Solving Applications Using Matrices......Page 948
A. Equality of Matrices......Page 953
B. Addition and Subtraction of Matrices......Page 955
C. Matrices and Multiplication......Page 956
A. Multiplication and Identity Matrices......Page 965
B. The Inverse of a Matrix......Page 967
C. Solving Systems Using Matrix Equations......Page 969
D. Determinants and Singular Matrices......Page 970
A. Solving Systems Using Determinants and Cramer’s Rule......Page 981
B. Determinants, Geometry, and the Coordinate Plane......Page 984
C. More on Partial Fraction Decomposition......Page 985
D. Solving Static Systems with Varying Constraints......Page 986
E. Using Matrices to Encrypt Messages......Page 988
Making Connections......Page 995
Summary and Concept Review......Page 996
Practice Test......Page 1001
Calculator Exploration and Discovery: Cramer’s Rule......Page 1002
Strengthening Core Skills: Augmented Matrices and Matrix Inverses......Page 1003
Cumulative Review: Chapters 1–9......Page 1004
Connections to Calculus: More on Partial Fraction Decomposition; The Geometry of Vectors and Determinants......Page 1006
CHAPTER 10 Analytical Geometry and the Conic Sections......Page 1009
A. Verifying Relationships from Plane Geometry......Page 1010
B. The Distance Between a Point and a Line......Page 1011
C. Characteristics of the Conic Sections......Page 1012
A. The Equation and Graph of a Circle......Page 1017
B. The Equation of an Ellipse......Page 1018
C. The Foci of an Ellipse......Page 1022
D. Applications Involving Foci......Page 1026
A. The Equation of a Hyperbola......Page 1032
B. Distinguishing Between the Equations of Circles, Ellipses, and Hyperbolas......Page 1037
C. The Foci of a Hyperbola......Page 1038
D. Applications Involving Foci......Page 1040
A. Parabolas with a Horizontal Axis......Page 1045
B. The Focus-Directrix Form of the Equation of a Parabola......Page 1047
C. Application of the Analytic Parabola......Page 1050
Reinforcing Basic Concepts: More on Completing the Square......Page 1054
A. Possible Solutions for a Nonlinear System......Page 1055
B. Solving Nonlinear Systems by Substitution......Page 1056
C. Solving Nonlinear Systems by Elimination......Page 1058
D. Solving Systems of Nonlinear Inequalities......Page 1060
E. Solving Applications of Nonlinear Systems......Page 1061
A. Plotting Points Using Polar Coordinates......Page 1066
B. Expressing a Point in Polar Coordinates......Page 1068
C. Converting Between Polar Coordinates and Rectangular Coordinates......Page 1069
D. Basic Polar Graphs and r-Value Analysis......Page 1072
E. Symmetry and Families of Polar Graphs......Page 1075
A. Rotated Conics and the Rotation of Axes......Page 1083
B. Identifying Conics Using the Discriminant......Page 1088
C. Conic Equations in Polar Form......Page 1090
D. Applications of Conics in Polar Form......Page 1092
A. Sketching a Curve Defined Parametrically......Page 1099
B. Writing Parametric Equations in Rectangular Form......Page 1102
C. Graphing Curves from the Cycloid Family......Page 1103
D. Common Applications of Parametric Equations......Page 1105
Summary and Concept Review......Page 1112
Practice Test......Page 1117
Calculator Exploration and Discovery: Elongation and Eccentricity......Page 1118
Strengthening Core Skills: Ellipses and Hyperbolas with Rational/Irrational Values of a and b......Page 1119
Cumulative Review: Chapters 1–10......Page 1120
Connections to Calculus: Polar Graphs and Instantaneous Rates of Change; Systems of Polar Equations......Page 1121
CHAPTER 11 Additional Topics in Algebra......Page 1125
A. Finding the Terms of a Sequence Given the General Term......Page 1126
B. Recursive Sequences and Factorial Notation......Page 1128
C. Series and Partial Sums......Page 1129
D. Summation Notation......Page 1130
E. Applications of Sequences......Page 1132
A. Identifying an Arithmetic Sequence and Finding the Common Difference......Page 1137
B. Finding the nth Term of an Arithmetic Sequence......Page 1138
C. Finding the nth Partial Sum of an Arithmetic Sequence......Page 1141
D. Applications......Page 1143
A. Geometric Sequences......Page 1146
B. Find the nth Term of a Geometric Sequence......Page 1147
C. Find the nth Partial Sum of a Geometric Sequence......Page 1151
D. The Sum of an Infinite Geometric Series......Page 1152
E. Applications Involving Geometric Sequences and Series......Page 1153
B. Mathematical Induction Applied to Sums......Page 1160
C. The General Principle of Mathematical Induction......Page 1163
Reinforcing Basic Concepts: Applications of Summation......Page 1167
A. Counting by Listing and Tree Diagrams......Page 1168
B. Fundamental Principle of Counting......Page 1170
C. Distinguishable Permutations......Page 1171
E. Combinations......Page 1173
A. Defining an Event......Page 1180
B. Elementary Probability......Page 1181
C. Properties of Probability......Page 1182
D. Probability and Quick-Counting......Page 1184
E. Probability and Nonexclusive Events......Page 1185
A. Binomial Powers and Pascal’s Triangle......Page 1193
B. Binomial Coefficients and Factorials......Page 1195
C. The Binomial Theorem......Page 1197
E. Applications......Page 1198
Making Connections......Page 1201
Summary and Concept Review......Page 1202
Practice Test......Page 1206
Calculator Exploration and Discovery: Infinite Series, Finite Results......Page 1208
Strengthening Core Skills: Probability, Quick-Counting, and Card Games......Page 1209
Cumulative Review: Chapters 1–11......Page 1210
Connections to Calculus: Applications of Summation......Page 1213
CHAPTER 12 Bridges to Calculus: An Introduction to Limits......Page 1217
A. Distinguishing between Limits and Approximations......Page 1218
B. Estimating Limits Using Tables and Graphs......Page 1219
C. One-Sided Limits......Page 1221
D. Limits That Fail to Exist......Page 1223
A. Establishing the Limit Properties......Page 1228
B. Finding Limits Using the Limit Properties......Page 1231
C. Distinguishing between a Declarative Statement and a Proof......Page 1234
Mid-Chapter Check......Page 1238
A. Continuity and Finding Limits by Direct Substitution......Page 1239
B. Evaluating Limits Using Algebra and Limit Properties......Page 1241
C. Evaluating Limits at Infinity......Page 1243
D. Evaluating Limits Graphically......Page 1247
12.4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve......Page 1251
A. The Limit of a Difference Quotient......Page 1252
B. Limits and the Area under a Curve......Page 1258
Making Connections......Page 1263
Summary and Concept Review......Page 1264
Practice Test......Page 1266
Calculator Exploration and Discovery: Technology and the Area Under a Curve......Page 1267
Cumulative Review: Chapters 1–12......Page 1268
A.1 Algebraic Expressions and the Properties of Real Numbers......Page 1271
A.2 Exponents, Scientific Notation, and a Review of Polynomials......Page 1280
A.3 Solving Linear Equations and Inequalities......Page 1294
A.4 Factoring Polynomials and Solving Polynomial Equations by Factoring......Page 1308
A.5 Rational Expressions and Equations......Page 1322
A.6 Radicals, Rational Exponents, and Radical Equations......Page 1334
Overview of Appendix A......Page 1350
Practice Test......Page 1352
Appendix B: Proof Positive—A Selection of Proofs from Precalculus......Page 1354
Appendix C: More on Synthetic Division......Page 1359
Appendix D: Reduced Row-Echelon Form and More on Matrices......Page 1361
Appendix E: The Equation of a Conic......Page 1363
Appendix F: Families of Polar Curves......Page 1365
Student Answer Appendix (SE only)......Page 1367
Index......Page 1447