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Precalculus

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Precalculus

This precalculus textmap is intended for college-level Precalculus students and is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text.

PrecalculusMathematics
Author
Jay Abramson
Publisher
OpenStax
Source
LibreTexts
License
CC BY
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 197 sections
  1. 01: Functions
  2. 1.01: Introduction to Functions
  3. 1.02: Functions and Function Notation
  4. 1.03: Domain and Range
  5. 1.04: Rates of Change and Behavior of Graphs
  6. 1.05: Composition of Functions
  7. 1.06: Transformation of Functions
  8. 1.07: Absolute Value Functions
  9. 1.08: Inverse Functions
  10. 1.09: Chapter Review
  11. 1.9.01: Key Terms
  12. 1.9.02: Key Equations
  13. 1.9.03: Key Concepts
  14. 1.10: Exercises
  15. 1.10.01: Review Exercises
  16. 1.10.02: Practice Test
  17. 02: Linear Functions
  18. 2.01: Introduction to Linear Functions
  19. 2.02: Linear Functions
  20. 2.03: Graphs of Linear Functions
  21. 2.04: Modeling with Linear Functions
  22. 2.05: Fitting Linear Models to Data
  23. 2.06: Chapter Review
  24. 2.6.01: Key Terms
  25. 2.6.02: Key Equations
  26. 2.6.03: Key Concepts
  27. 2.07: Exercises
  28. 2.7.01: Review Exercises
  29. 2.7.02: Practice Test
  30. 03: Polynomial and Rational Functions
  31. 3.01: Introduction to Polynomial and Rational Functions
  32. 3.02: Complex Numbers
  33. 3.03: Quadratic Functions
  34. 3.04: Power Functions and Polynomial Functions
  35. 3.05: Graphs of Polynomial Functions
  36. 3.06: Dividing Polynomials
  37. 3.07: Zeros of Polynomial Functions
  38. 3.08: Rational Functions
  39. 3.09: Inverses and Radical Functions
  40. 3.10: Modeling Using Variation
  41. 3.11: Chapter Review
  42. 3.11.01: Key Terms
  43. 3.11.02: Key Equations
  44. 3.11.03: Key Concepts
  45. 3.12: Exercises
  46. 3.12.01: Review Exercises
  47. 3.12.02: Practice Test
  48. 04: Exponential and Logarithmic Functions
  49. 4.01: Introduction to Exponential and Logarithmic Functions
  50. 4.02: Exponential Functions
  51. 4.03: Graphs of Exponential Functions
  52. 4.04: Logarithmic Functions
  53. 4.05: Graphs of Logarithmic Functions
  54. 4.06: Logarithmic Properties
  55. 4.07: Exponential and Logarithmic Equations
  56. 4.08: Exponential and Logarithmic Models
  57. 4.09: Fitting Exponential Models to Data
  58. 4.10: Chapter Review
  59. 4.10.01: Key Terms
  60. 4.10.02: Key Equations
  61. 4.10.03: Key Concepts
  62. 4.11: Exercises
  63. 4.11.01: Review Exercises
  64. 4.11.02: Practice Test
  65. 05: Trigonometric Functions
  66. 5.01: Introduction to Trigonometric Functions
  67. 5.02: Angles
  68. 5.03: Unit Circle - Sine and Cosine Functions
  69. 5.04: The Other Trigonometric Functions
  70. 5.05: Right Triangle Trigonometry
  71. 5.06: Chapter Review
  72. 5.6.01: Key Terms
  73. 5.6.02: Key Equations
  74. 5.6.03: Key Concepts
  75. 5.07: Exercises
  76. 5.7.01: Review Exercises
  77. 5.7.02: Practice Test
  78. 06: Periodic Functions
  79. 6.01: Introduction to Periodic Functions
  80. 6.02: Graphs of the Sine and Cosine Functions
  81. 6.03: Graphs of the Other Trigonometric Functions
  82. 6.04: Inverse Trigonometric Functions
  83. 6.05: Chapter Review
  84. 6.5.01: Key Terms
  85. 6.5.02: Key Equations
  86. 6.5.03: Key Concepts
  87. 6.06: Exercises
  88. 6.6.01: Review Exercises
  89. 6.6.02: Practice Test
  90. 07: Trigonometric Identities and Equations
  91. 7.01: Introduction to Trigonometric Identities and Equations
  92. 7.02: Solving Trigonometric Equations with Identities
  93. 7.03: Sum and Difference Identities
  94. 7.04: Double-Angle Half-Angle and Reduction Formulas
  95. 7.05: Sum-to-Product and Product-to-Sum Formulas
  96. 7.06: Solving Trigonometric Equations
  97. 7.07: Modeling with Trigonometric Functions
  98. 7.08: Chapter Review
  99. 7.8.01: Key Terms
  100. 7.8.02: Key Equations
  101. 7.8.03: Key Concepts
  102. 7.09: Exercises
  103. 7.9.01: Review Exercises
  104. 7.9.02: Practice Test
  105. 08: Further Applications of Trigonometry
  106. 8.01: Introduction to Further Applications of Trigonometry
  107. 8.02: Non-right Triangles - Law of Sines
  108. 8.03: Non-right Triangles - Law of Cosines
  109. 8.04: Polar Coordinates
  110. 8.05: Polar Coordinates - Graphs
  111. 8.06: Polar Form of Complex Numbers
  112. 8.07: Parametric Equations
  113. 8.08: Parametric Equations - Graphs
  114. 8.09: Vectors
  115. 8.10: Chapter Review
  116. 8.10.01: Key Terms
  117. 8.10.02: Key Equations
  118. 8.10.03: Key Concepts
  119. 8.11: Exercises
  120. 8.11.01: Review Exercises
  121. 8.11.02: Practice Test
  122. 09: Systems of Equations and Inequalities
  123. 9.01: Introduction to Systems of Equations and Inequalities
  124. 9.02: Systems of Linear Equations - Two Variables
  125. 9.03: Systems of Linear Equations - Three Variables
  126. 9.04: Systems of Nonlinear Equations and Inequalities - Two Variables
  127. 9.05: Partial Fractions
  128. 9.06: Matrices and Matrix Operations
  129. 9.07: Solving Systems with Gaussian Elimination
  130. 9.08: Solving Systems with Inverses
  131. 9.09: Solving Systems with Cramer's Rule
  132. 9.10: Chapter Review
  133. 9.10.01: Key Terms
  134. 9.10.02: Key Equations
  135. 9.10.03: Key Concepts
  136. 9.11: Exercises
  137. 9.11.01: Review Exercises
  138. 9.11.02: Practice Test
  139. 10: Analytic Geometry
  140. 10.01: Introduction to Analytic Geometry
  141. 10.02: The Ellipse
  142. 10.03: The Hyperbola
  143. 10.04: The Parabola
  144. 10.05: Rotation of Axes
  145. 10.06: Conic Sections in Polar Coordinates
  146. 10.07: Chapter Review
  147. 10.7.01: Key Terms
  148. 10.7.02: Key Equations
  149. 10.7.03: Key Concepts
  150. 10.08: Exercises
  151. 10.8.01: Review Exercises
  152. 10.8.02: Practice Test
  153. 10.8.3: Answers to Questions
  154. 11: Sequences Probability and Counting Theory
  155. 11.01: Introduction to Sequences Probability and Counting Theory
  156. 11.02: Sequences and Their Notations
  157. 11.03: Arithmetic Sequences
  158. 11.04: Geometric Sequences
  159. 11.05: Series and Their Notations
  160. 11.06: Counting Principles
  161. 11.07: Binomial Theorem
  162. 11.08: Probability
  163. 11.09: Chapter Review
  164. 11.9.01: Key Terms
  165. 11.9.02: Key Equations
  166. 11.9.03: Key Concepts
  167. 11.10: Exercises
  168. 11.10.01: Review Exercises
  169. 11.10.02: Practice Test
  170. 12: Introduction to Calculus
  171. 12.01: Introduction to Calculus
  172. 12.02: Finding Limits - Numerical and Graphical Approaches
  173. 12.03: Finding Limits - Properties of Limits
  174. 12.04: Continuity
  175. 12.05: Derivatives
  176. 12.06: Chapter Review
  177. 12.6.01: Key Terms
  178. 12.6.02: Key Equations
  179. 12.6.03: Key Concepts
  180. 12.07: Exercises
  181. 12.7.01: Review Exercises
  182. 12.7.02: Practice Test
  183. 13: Appendix
  184. 13.01: Basic Functions and Identities
  185. 13.02: Answer Key
  186. 13.2.01: Chapter 1
  187. 13.2.02: Chapter 2
  188. 13.2.03: Chapter 3
  189. 13.2.04: Chapter 4
  190. 13.2.05: Chapter 5
  191. 13.2.06: Chapter 6
  192. 13.2.07: Chapter 7
  193. 13.2.08: Chapter 8
  194. 13.2.09: Chapter 9
  195. 13.2.10: Chapter 10
  196. 13.2.11: Chapter 11
  197. 13.2.12: Chapter 12