College Algebra 2e with Corequisite Support

1292 Pages·2021·85.754 MB·English

by  OpenStax

College Algebra with
Corequisite Support 2e
SENIOR CONTRIBUTING AUTHORS
JAY ABRAMSON, ARIZONA STATE UNIVERSITY
SHARON NORTH, ST. LOUIS COMMUNITY COLLEGE
OpenStax
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DIGITAL VERSION ISBN-13 978-1-951693-46-6
ORIGINAL PUBLICATION YEAR 2021
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Contents
Preface 1
1 Prerequisites 7
Introduction to Prerequisites 7
1.1Real Numbers: Algebra Essentials 7
1.2Exponents and Scientific Notation 27
1.3Radicals and Rational Exponents 45
1.4Polynomials 57
1.5Factoring Polynomials 68
1.6Rational Expressions 80
Chapter Review 91
Exercises 94
2 Equations and Inequalities 99
Introduction to Equations and Inequalities 99
2.1The Rectangular Coordinate Systems and Graphs 99
2.2Linear Equations in One Variable 116
2.3Models and Applications 136
2.4Complex Numbers 148
2.5Quadratic Equations 161
2.6Other Types of Equations 178
2.7Linear Inequalities and Absolute Value Inequalities 190
Chapter Review 201
Exercises 204
3 Functions 209
Introduction to Functions 209
3.1Functions and Function Notation 209
3.2Domain and Range 237
3.3Rates of Change and Behavior of Graphs 258
3.4Composition of Functions 277
3.5Transformation of Functions 295
3.6Absolute Value Functions 333
3.7Inverse Functions 343
Chapter Review 361
Exercises 365
4 Linear Functions 375
Introduction to Linear Functions 375
4.1Linear Functions 375
4.2Modeling with Linear Functions 415
4.3Fitting Linear Models to Data 432
Chapter Review 448
Exercises 449
5 Polynomial and Rational Functions 459
Introduction to Polynomial and Rational Functions 459
5.1Quadratic Functions 460
5.2Power Functions and Polynomial Functions 483
5.3Graphs of Polynomial Functions 506
5.4Dividing Polynomials 530
5.5Zeros of Polynomial Functions 544
5.6Rational Functions 559
5.7Inverses and Radical Functions 586
5.8Modeling Using Variation 603
Chapter Review 616
Exercises 620
6 Exponential and Logarithmic Functions 625
Introduction to Exponential and Logarithmic Functions 625
6.1Exponential Functions 626
6.2Graphs of Exponential Functions 648
6.3Logarithmic Functions 665
6.4Graphs of Logarithmic Functions 677
6.5Logarithmic Properties 704
6.6Exponential and Logarithmic Equations 720
6.7Exponential and Logarithmic Models 736
6.8Fitting Exponential Models to Data 760
Chapter Review 780
Exercises 785
7 Systems of Equations and Inequalities 795
Introduction to Systems of Equations and Inequalities 795
7.1Systems of Linear Equations: Two Variables 796
7.2Systems of Linear Equations: Three Variables 819
7.3Systems of Nonlinear Equations and Inequalities: Two Variables 836
7.4Partial Fractions 854
7.5Matrices and Matrix Operations 868
7.6Solving Systems with Gaussian Elimination 884
7.7Solving Systems with Inverses 901
7.8Solving Systems with Cramer's Rule 919
Chapter Review 935
Exercises 938
8 Analytic Geometry 945
Introduction to Analytic Geometry 945
8.1The Ellipse 946
8.2The Hyperbola 966
8.3The Parabola 988
8.4Rotation of Axes 1009
8.5Conic Sections in Polar Coordinates 1027
Chapter Review 1038
Exercises 1040
9 Sequences, Probability, and Counting Theory 1045
Introduction to Sequences, Probability and Counting Theory 1045
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9.1Sequences and Their Notations 1045
9.2Arithmetic Sequences 1063
9.3Geometric Sequences 1079
9.4Series and Their Notations 1092
9.5Counting Principles 1109
9.6Binomial Theorem 1122
9.7Probability 1132
Chapter Review 1144
Exercises 1147
Answer Key 1155
Index 1279
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