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Precalculus

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Precalculus

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.

PrecalculusMathematics
Tác giả
Thomas Tradler and Holly Carley
Nhà xuất bản
CUNY New York City College of Technology
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LibreTexts
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CC BY-NC-SA
Ngôn ngữ
EN
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Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 119 mục
  1. 01: The Absolute Value
  2. 1.01: Background regarding numbers
  3. 1.02: The absolute value
  4. 1.03: Inequalities and intervals
  5. 1.04: Absolute value inequalities
  6. 1.05: Exercises
  7. 02: Lines and Functions
  8. 2.01: Lines slope and intercepts
  9. 2.02: Introduction to functions
  10. 2.03: Exercises
  11. 03: Functions by Formulas and Graphs
  12. 3.01: Functions given by formulas
  13. 3.02: Functions given by graphs
  14. 3.03: Exercises
  15. 04: Introduction to the TI-84
  16. 4.01: Graphing with the TI-84
  17. 4.02: Finding zeros maxima and minima
  18. 4.03: Exercises
  19. 05: Basic Functions and Transformations
  20. 5.01: Graphing Basic Functions
  21. 5.02: Transformation of Graphs
  22. 5.03: Exercises
  23. 06: Operations on Functions
  24. 6.01: Operations on functions given by formulas
  25. 6.02: Operations on functions given by tables
  26. 6.03: Exercises
  27. 07: The Inverse of a Function
  28. 7.01: One-to-one functions
  29. 7.02: Inverse function
  30. 7.03: Exercises
  31. 08: Dividing Polynomials
  32. 8.01: Long division
  33. 8.02: Dividing by (x - c)
  34. 8.03: Optional section- Synthetic division
  35. 8.04: Exercises
  36. 09: Graphing Polynomials
  37. 9.01: Graphs of polynomials
  38. 9.02: Finding roots of a polynomial with the TI-84
  39. 9.03: Optional Section- Graphing Polynomials by Hand
  40. 9.04: Exercises
  41. 10: Roots of Polynomials
  42. 10.01: Optional section- The rational root theorem
  43. 10.02: The Fundamental Theorem of Algebra
  44. 10.03: Exercises
  45. 11: Rational Functions
  46. 11.01: Graphs of rational functions
  47. 11.02: Optional section- Rational functions by hand
  48. 11.03: Exercises
  49. 12: Polynomial and Rational Inequalities
  50. 12.01: Polynomial Inequalities
  51. 12.02: Rational inequalities and absolute value inequalities
  52. 12.03: Exercises
  53. 13: Exponential and Logarithmic Functions
  54. 13.01: Exponential functions and their graphs
  55. 13.02: Logarithmic functions and their graphs
  56. 13.03: Exercises
  57. 14: Properties of Exponentials and Logarithms
  58. 14.01: Algebraic Properties of exp and log
  59. 14.02: Solving Exponential and Logarithmic Equations
  60. 14.03: Exercises
  61. 15: Applications Exponentials and Logarithms
  62. 15.01: Applications of exponential functions
  63. 15.02: Exercises
  64. 16: Half-life and Compound Interest
  65. 16.01: Half-life
  66. 16.02: Compound Interest
  67. 16.03: Exercises
  68. 17: Trigonometric Functions
  69. 17.01: Basic trigonometric definitions and facts
  70. 17.02: sin cos and tan as functions
  71. 17.03: Exercises
  72. 18: Addition of Angles and Multiple Angles
  73. 18.01: Addition and subtraction of angles
  74. 18.02: Double and half angles
  75. 18.03: Exercises
  76. 19: Inverse Trigonometric Functions
  77. 19.01: The functions of arcsin arccos and arctan
  78. 19.02: Exercises
  79. 20: Trigonometric Equations
  80. 20.01: Basic trigonometric equations
  81. 20.02: Equations involving trigonometric functions
  82. 20.03: Exercises
  83. 21: Complex Numbers
  84. 21.01: Polar Form of Complex Numbers
  85. 21.02: Multiplication and division of complex numbers
  86. 21.03: Exercises
  87. 22: Vectors in the Plane
  88. 22.01: Introduction to Vectors
  89. 22.02: Operations on vectors
  90. 22.03: Exercises
  91. 23: Sequences and Series
  92. 23.01: Introduction to Sequences and Series
  93. 23.02: The arithmetic sequence
  94. 23.03: Exercises
  95. 24: The Geometric Series
  96. 24.01: Finite Geometric Series
  97. 24.02: Infinite Geometric Series
  98. 24.03: Exercises
  99. 25: The Binomial Theorem
  100. 25.01: The Binomial Theorem
  101. 25.02: Binomial Expansion
  102. 25.03: Exercises
  103. 26: Appendix A - Introduction to the TI-84
  104. 26.01: A.1- Basic calculator functions
  105. 26.02: A.2 Graphing a function
  106. 26.03: A.3- Graphing more than one function
  107. 26.04: A.4- Graphing a piecewise defined function
  108. 26.05: A.5- Using the table
  109. 26.06: A.6- Solving an equation using the solver
  110. 26.07: A.7- Special functions (absolute value n-th root etc.)
  111. 26.08: A.8- Programming the calculator
  112. 26.09: A.9- Common errors
  113. 26.10: A.10- Resetting the calculator to factory settings
  114. 27: Reviews
  115. 27.01: Review of functions and graphs
  116. 27.02: Review of polynomials and rational functions
  117. 27.03: Review of exponential and logarithmic functions
  118. 27.04: Review of trigonometric functions
  119. 27.05: Review of complex numbers sequences and the binomial theorem