Precalculus 2e 2021

1972 Pages·2021·25.178 MB·English

by  Jay Abramson

Precalculus 2e
SENIOR CONTRIBUTING AUTHOR
JAY ABRAMSON, ARIZONA STATE UNIVERSITY
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HARDCOVER BOOK ISBN-13 978-1-711494-00-5
B&W PAPERBACK BOOK ISBN-13 978-1-711493-99-2
DIGITAL VERSION ISBN-13 978-1-951693-39-8
ORIGINAL PUBLICATION YEAR 2021
1 2 3 4 5 6 7 8 9 10 RS 21
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Contents
Preface 1
1 Functions 7
Introduction to Functions 7
1.1Functions and Function Notation 7
1.2Domain and Range 34
1.3Rates of Change and Behavior of Graphs 56
1.4Composition of Functions 73
1.5Transformation of Functions 89
1.6Absolute Value Functions 121
1.7Inverse Functions 133
Chapter Review 149
Exercises 153
2 Linear Functions 163
Introduction to Linear Functions 163
2.1Linear Functions 164
2.2Graphs of Linear Functions 186
2.3Modeling with Linear Functions 211
2.4Fitting Linear Models to Data 225
Chapter Review 239
Exercises 240
3 Polynomial and Rational Functions 251
Introduction to Polynomial and Rational Functions 251
3.1Complex Numbers 252
3.2Quadratic Functions 262
3.3Power Functions and Polynomial Functions 283
3.4Graphs of Polynomial Functions 302
3.5Dividing Polynomials 325
3.6Zeros of Polynomial Functions 336
3.7Rational Functions 350
3.8Inverses and Radical Functions 376
3.9Modeling Using Variation 389
Chapter Review 399
Exercises 403
4 Exponential and Logarithmic Functions 409
Introduction to Exponential and Logarithmic Functions 409
4.1Exponential Functions 410
4.2Graphs of Exponential Functions 429
4.3Logarithmic Functions 443
4.4Graphs of Logarithmic Functions 452
4.5Logarithmic Properties 474
4.6Exponential and Logarithmic Equations 486
4.7Exponential and Logarithmic Models 499
4.8Fitting Exponential Models to Data 518
Chapter Review 534
Exercises 539
5 Trigonometric Functions 549
Introduction to Trigonometric Functions 549
5.1Angles 550
5.2Unit Circle: Sine and Cosine Functions 573
5.3The Other Trigonometric Functions 594
5.4Right Triangle Trigonometry 610
Chapter Review 623
Exercises 626
6 Periodic Functions 631
Introduction to Periodic Functions 631
6.1Graphs of the Sine and Cosine Functions 631
6.2Graphs of the Other Trigonometric Functions 651
6.3Inverse Trigonometric Functions 672
Chapter Review 685
Exercises 686
7 Trigonometric Identities and Equations 693
Introduction to Trigonometric Identities and Equations 693
7.1Solving Trigonometric Equations with Identities 693
7.2Sum and Difference Identities 704
7.3Double-Angle, Half-Angle, and Reduction Formulas 719
7.4Sum-to-Product and Product-to-Sum Formulas 732
7.5Solving Trigonometric Equations 740
7.6Modeling with Trigonometric Functions 755
Chapter Review 777
Exercises 781
8 Further Applications of Trigonometry 787
Introduction to Further Applications of Trigonometry 787
8.1Non-right Triangles: Law of Sines 787
8.2Non-right Triangles: Law of Cosines 805
8.3Polar Coordinates 819
8.4Polar Coordinates: Graphs 833
8.5Polar Form of Complex Numbers 852
8.6Parametric Equations 863
8.7Parametric Equations: Graphs 876
8.8Vectors 888
Chapter Review 910
Exercises 914
9 Systems of Equations and Inequalities 921
Introduction to Systems of Equations and Inequalities 921
9.1Systems of Linear Equations: Two Variables 922
9.2Systems of Linear Equations: Three Variables 941
9.3Systems of Nonlinear Equations and Inequalities: Two Variables 953
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9.4Partial Fractions 965
9.5Matrices and Matrix Operations 975
9.6Solving Systems with Gaussian Elimination 988
9.7Solving Systems with Inverses 1002
9.8Solving Systems with Cramer's Rule 1017
Chapter Review 1030
Exercises 1033
10 Analytic Geometry 1041
Introduction to Analytic Geometry 1041
10.1The Ellipse 1042
10.2The Hyperbola 1058
10.3The Parabola 1075
10.4Rotation of Axes 1091
10.5Conic Sections in Polar Coordinates 1106
Chapter Review 1117
Exercises 1119
11 Sequences, Probability and Counting Theory 1125
Introduction to Sequences, Probability and Counting Theory 1125
11.1Sequences and Their Notations 1125
11.2Arithmetic Sequences 1140
11.3Geometric Sequences 1152
11.4Series and Their Notations 1161
11.5Counting Principles 1175
11.6Binomial Theorem 1186
11.7Probability 1193
Chapter Review 1204
Exercises 1207
12 Introduction to Calculus 1215
Introduction to Calculus 1215
12.1Finding Limits: Numerical and Graphical Approaches 1215
12.2Finding Limits: Properties of Limits 1227
12.3Continuity 1237
12.4Derivatives 1252
Chapter Review 1275
Exercises 1277
A Basic Functions and Identities 1283
Answer Key 1287
Index 1447
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