Precalculus

by Thomas Tradler and Holly Carley

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These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY. Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use.

Description from LibreTexts.

Publisher
CUNY New York City College of Technology
Subjects
Mathematics, Precalculus
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: The Absolute Value
  7. 1.1: Background regarding numbers
  8. 1.2: The absolute value
  9. 1.3: Inequalities and intervals
  10. 1.4: Absolute value inequalities
  11. 1.5: Exercises
  12. 2: Lines and Functions
  13. 2.1: Lines, slope and intercepts
  14. 2.2: Introduction to functions
  15. 2.3: Exercises
  16. 3: Functions by Formulas and Graphs
  17. 3.1: Functions given by formulas
  18. 3.2: Functions given by graphs
  19. 3.3: Exercises
  20. 4: Introduction to the TI-84
  21. 4.1: Graphing with the TI-84
  22. 4.2: Finding zeros, maxima, and minima
  23. 4.3: Exercises
  24. 5: Basic Functions and Transformations
  25. 5.1: Graphing Basic Functions
  26. 5.2: Transformation of Graphs
  27. 5.3: Exercises
  28. 6: Operations on Functions
  29. 6.1: Operations on functions given by formulas
  30. 6.2: Operations on functions given by tables
  31. 6.3: Exercises
  32. 7: The Inverse of a Function
  33. 7.1: One-to-one functions
  34. 7.2: Inverse function
  35. 7.3: Exercises
  36. 8: Dividing Polynomials
  37. 8.1: Long division
  38. 8.2: Dividing by (x - c)
  39. 8.3: Optional section- Synthetic division
  40. 8.4: Exercises
  41. 9: Graphing Polynomials
  42. 9.1: Graphs of polynomials
  43. 9.2: Finding roots of a polynomial with the TI-84
  44. 9.3: Optional Section- Graphing Polynomials by Hand
  45. 9.4: Exercises
  46. 10: Roots of Polynomials
  47. 10.1: Optional section- The rational root theorem
  48. 10.2: The Fundamental Theorem of Algebra
  49. 10.3: Exercises
  50. 11: Rational Functions
  51. 11.1: Graphs of rational functions
  52. 11.2: Optional section- Rational functions by hand
  53. 11.3: Exercises
  54. 12: Polynomial and Rational Inequalities
  55. 12.1: Polynomial Inequalities
  56. 12.2: Rational inequalities and absolute value inequalities
  57. 12.3: Exercises
  58. 13: Exponential and Logarithmic Functions
  59. 13.1: Exponential functions and their graphs
  60. 13.2: Logarithmic functions and their graphs
  61. 13.3: Exercises
  62. 14: Properties of Exponentials and Logarithms
  63. 14.1: Algebraic Properties of exp and log
  64. 14.2: Solving Exponential and Logarithmic Equations
  65. 14.3: Exercises
  66. 15: Applications Exponentials and Logarithms
  67. 15.1: Applications of exponential functions
  68. 15.2: Exercises
  69. 16: Half-life and Compound Interest
  70. 16.1: Half-life
  71. 16.2: Compound Interest
  72. 16.3: Exercises
  73. 17: Trigonometric Functions
  74. 17.1: Basic trigonometric definitions and facts
  75. 17.2: sin, cos, and tan as functions
  76. 17.3: Exercises
  77. 18: Addition of Angles and Multiple Angles
  78. 18.1: Addition and subtraction of angles
  79. 18.2: Double and half angles
  80. 18.3: Exercises
  81. 19: Inverse Trigonometric Functions
  82. 19.1: The functions of arcsin, arccos, and arctan
  83. 19.2: Exercises
  84. 20: Trigonometric Equations
  85. 20.1: Basic trigonometric equations
  86. 20.2: Equations involving trigonometric functions
  87. 20.3: Exercises
  88. 21: Complex Numbers
  89. 21.1: Polar Form of Complex Numbers
  90. 21.2: Multiplication and division of complex numbers
  91. 21.3: Exercises
  92. 22: Vectors in the Plane
  93. 22.1: Introduction to Vectors
  94. 22.2: Operations on vectors
  95. 22.3: Exercises
  96. 23: Sequences and Series
  97. 23.1: Introduction to Sequences and Series
  98. 23.2: The arithmetic sequence
  99. 23.3: Exercises
  100. 24: The Geometric Series
  101. 24.1: Finite Geometric Series
  102. 24.2: Infinite Geometric Series
  103. 24.3: Exercises
  104. 25: The Binomial Theorem
  105. 25.1: The Binomial Theorem
  106. 25.2: Binomial Expansion
  107. 25.3: Exercises
  108. 26: Appendix A - Introduction to the TI-84
  109. 26.1: A.1- Basic calculator functions
  110. 26.2: A.2 Graphing a function
  111. 26.3: A.3- Graphing more than one function
  112. 26.4: A.4- Graphing a piecewise defined function
  113. 26.5: A.5- Using the table
  114. 26.6: A.6- Solving an equation using the solver
  115. 26.7: A.7- Special functions (absolute value, n-th root, etc.)
  116. 26.8: A.8- Programming the calculator
  117. 26.9: A.9- Common errors
  118. 26.10: A.10- Resetting the calculator to factory settings
  119. 27: Reviews
  120. 27.1: Review of functions and graphs
  121. 27.2: Review of polynomials and rational functions
  122. 27.3: Review of exponential and logarithmic functions
  123. 27.4: Review of trigonometric functions
  124. 27.5: Review of complex numbers, sequences, and the binomial theorem
  125. Back Matter
  126. Index
  127. Glossary
  128. Detailed Licensing