Algebra and Trigonometry

by Jay Abramson

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Algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.

Description from LibreTexts.

Publisher
Arizona State University
Subjects
Mathematics
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Prerequisites
  7. 1.1: Prelude to Prerequisites
  8. 1.2: Real Numbers - Algebra Essentials
  9. 1.2E: Real Numbers - Algebra Essentials (Exercises)
  10. 1.3: Exponents and Scientific Notation
  11. 1.3E: Exponents and Scientific Notation (Exercises)
  12. 1.4: Radicals and Rational Expressions
  13. 1.4E: Radicals and Rational Expressions (Exercise)
  14. 1.5: Polynomials
  15. 1.5E: Polynomials (Exercises)
  16. 1.6: Factoring Polynomials
  17. 1.6E: Factoring Polynomials (Exercises)
  18. 1.7: Rational Expressions
  19. 1.7E: Rational Expressions (Exercises)
  20. 2: Equations and Inequalities
  21. 2.1: Prelude to Equations and Inequalities
  22. 2.2: The Rectangular Coordinate Systems and Graphs
  23. 2.2E: The Rectangular Coordinate Systems and Graphs (Exercises)
  24. 2.3: Linear Equations in One Variable
  25. 2.3E: Linear Equations in One Variable (Exercises)
  26. 2.4: Complex Numbers
  27. 2.4E: Complex Numbers (Exercises)
  28. 2.5: Quadratic Equations
  29. 2.5E: Quadratic Equations (Exercises)
  30. 2.6: Other Types of Equations
  31. 2.6E: Other Types of Equations (Exercises)
  32. 2.7: Modeling with Equations
  33. 2.7.1: Models and Applications
  34. 2.7.1E: Models and Applications (Exercises)
  35. 2.7.2: Solve Mixture and Uniform Motion Applications
  36. 2.7.2E: Exercises
  37. 2.7.3: Solve Applications with Rational Equations
  38. 2.7.3E: Exercises
  39. 2.8: Linear and Absolute Value Inequalities
  40. 2.8.1: Linear Inequalities
  41. 2.8.1E: Exercises
  42. 2.8.2: Solve Absolute Value Inequalities
  43. 2.8.2E: Exercises
  44. 2.8E: Linear Inequalities and Absolute Value Inequalities (Exercises)
  45. 3: Functions
  46. 3.1: Prelude to Functions
  47. 3.2: Functions and Function Notation
  48. 3.2E: Functions and Function Notation (Exercises)
  49. 3.3: Domain and Range
  50. 3.3E: Domain and Range (Exercises)
  51. 3.4: Rates of Change and Behavior of Graphs
  52. 3.4E: Rates of Change and Behavior of Graphs (Exercises)
  53. 3.5: Linear Functions
  54. 3.5.1: Prelude to Linear Functions
  55. 3.5.2: Linear Functions
  56. 3.5.3: Graphs of Linear Functions
  57. 3.5.4: Modeling with Linear Functions
  58. 3.5.5: Fitting Linear Models to Data
  59. 3.5.E: Linear Functions(Exercises)
  60. 3.5.R: Linear Functions(Review)
  61. 3.6: Composition of Functions
  62. 3.6E: Composition of Functions (Exercises)
  63. 3.7: Transformation of Functions
  64. 3.7E: Transformation of Functions (Exercises)
  65. 3.8: Absolute Value Functions
  66. 3.8E: Absolute Value Functions (Exercises)
  67. 3.9: Inverse Functions
  68. 3.9E: Inverse Functions (Exercises)
  69. 4: Polynomial and Rational Functions
  70. 4.1: Prelude to Polynomial and Rational Functions
  71. 4.2: Quadratic Functions
  72. 4.2E: Quadratic Functions (Exercises)
  73. 4.3: Power Functions and Polynomial Functions
  74. 4.3E: Power Functions and Polynomial Functions (Exercises)
  75. 4.4: Graphs of Polynomial Functions
  76. 4.4E: Graphs of Polynomial Functions (Exercises)
  77. 4.5: Dividing Polynomials
  78. 4.5E: Dividing Polynomials (Exercises)
  79. 4.6: Zeros of Polynomial Functions
  80. 4.6E: Zeros of Polynomial Functions (Exercises)
  81. 4.7: Rational Functions
  82. 4.7E: Rational Functions (Exercises)
  83. 4.8: Non-linear Inequalities
  84. 4.8.1: Solve Quadratic Inequalities
  85. 4.8.1E: Exercises
  86. 4.8.2: Solve Rational Inequalities
  87. 4.8.2E: Exercises
  88. 5: Exponential and Logarithmic Functions
  89. 5.1: Prelude to Exponential and Logarithmic Functions
  90. 5.2: Exponential Functions
  91. 5.2E: Exponential Functions (Exercises)
  92. 5.3: Graphs of Exponential Functions
  93. 5.3E: Graphs of Exponential Functions (Exercises)
  94. 5.4: Logarithmic Functions
  95. 5.4E: Logarithmic Functions (Exercises)
  96. 5.5: Graphs of Logarithmic Functions
  97. 5.5E: Graphs of Logarithmic Functions (Exercises)
  98. 5.6: Logarithmic Properties
  99. 5.6E: Logarithmic Properties (Exercises)
  100. 5.7: Exponential and Logarithmic Equations
  101. 5.7E: Exponential and Logarithmic Equations (Exercises)
  102. 5.8: Exponential and Logarithmic Models
  103. 5.8E: Exponential and Logarithmic Models (Exercises)
  104. 5.9: Fitting Exponential Models to Data
  105. 5.9E: Fitting Exponential Models to Data (Exercises)
  106. 6: Systems of Equations and Inequalities
  107. 6.1: Prelude to Systems of Equations and Inequalities
  108. 6.2: Systems of Linear Equations - Two Variables
  109. 6.2E: Systems of Linear Equations - Two Variables (Exercises)
  110. 6.3: Systems of Linear Equations with Three Variables
  111. 6.3E: Systems of Linear Equations with Three Variables (Exercises)
  112. 6.4: Systems of Nonlinear Equations and Inequalities - Two Variables
  113. 6.4E: Systems of Nonlinear Equations and Inequalities - Two Variables (Exercises)
  114. 6.5: Solving Systems with Gaussian Elimination
  115. 6.5E: Solving Systems with Gaussian Elimination (Exercises)
  116. 7: Analytic Geometry
  117. 7.1: Prelude to Analytic Geometry
  118. 7.2: The Parabola
  119. 7.2E: The Parabola (Exercises)
  120. 7.3: The Ellipse
  121. 7.3E: The Ellipse (Exercises)
  122. 7.4: The Hyperbola
  123. 7.4E: The Hyperbola (Exercises)
  124. 8: Sequences, Probability, and Counting Theory
  125. 8.1: Prelude to Sequences, Probability and Counting Theory
  126. 8.2: Sequences and Their Notations
  127. 8.2E: Sequences and Their Notations (Exercises)
  128. 8.3: Arithmetic Sequences
  129. 8.3E: Arithmetic Sequences (Exercises)
  130. 8.4: Geometric Sequences
  131. 8.4E: Geometric Sequences (Exercises)
  132. 8.5: Series and Their Notations
  133. 8.5E: Series and Their Notations (Exercises)
  134. 9: Additional Topics for Ch 4, 6, 7 and 8
  135. 9.1: Inverses and Radical Functions
  136. 9.1.1: Inverses and Radical Functions (Exercises)
  137. 9.2: Modeling Using Variation
  138. 9.2E: Modeling Using Variation (Exercises)
  139. 9.3: Partial Fractions
  140. 9.3.1: Partial Fractions (Exercises)
  141. 9.4: Matrices and Matrix Operations
  142. 9.4E: Matrices and Matrix Operations (Exercises)
  143. 9.5: Solving Systems with Inverses
  144. 9.5E: Solving Systems with Inverses (Exercises)
  145. 9.6: Solving Systems with Cramer's Rule
  146. 9.6E: Solving Systems with Cramer's Rule (Exercises)
  147. 9.7: Rotation of Axes
  148. 9.7E: Rotation of Axes (Exercises)
  149. 9.8: Conic Sections in Polar Coordinates
  150. 9.8E: Conic Sections in Polar Coordinates (Exercises)
  151. 9.9: Counting Principles
  152. 9.9E: Counting Principles (Exercises)
  153. 9.10: Binomial Theorem
  154. 9.10E: Binomial Theorem (Exercises)
  155. 9.11: Probability
  156. 9.11E: Probability (Exercises)
  157. Back Matter
  158. Index
  159. Glossary
  160. Detailed Licensing