Working with Functions - Comprehensive Course on Domain, Range, Notation, and Graph Transformations

Working with Functions - Comprehensive Course on Domain, Range, Notation, and Graph Transformations

Eddie Woo via YouTube Direct link

Domain & Range

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Domain & Range

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Working with Functions - Comprehensive Course on Domain, Range, Notation, and Graph Transformations

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  1. 1 Domain & Range
  2. 2 Function Notation
  3. 3 Functions and Relations
  4. 4 Odd & Even Functions
  5. 5 Even Functions - example proof
  6. 6 Difference of Squares and Cubes
  7. 7 Linear Equation with No Solution?
  8. 8 Manipulating Linear, Quadratic & Cubic Identities
  9. 9 Extraneous Solutions
  10. 10 Completing the Square: Why and How
  11. 11 Solving Simultaneous Equations by Elimination
  12. 12 Solving Simultaneous Equations by Substitution
  13. 13 Visual Representation of Solving Simultaneous Equations
  14. 14 What is Absolute Value? (1 of 3: The Simplest Definition)
  15. 15 What is Absolute Value? (2 of 3: Two Algebraic Definitions)
  16. 16 Graphing y = |x| from its Algebraic Definition
  17. 17 What is Absolute Value? (3 of 3: The Geometric Definition)
  18. 18 Finding a Function's Range from its Domain
  19. 19 Absolute Value Graphs (1 of 2: Understanding Shifts)
  20. 20 Absolute Value Graphs (2 of 2: Adding Graphs)
  21. 21 How to Graph |x| + |y| = 1
  22. 22 Solving Equations w/ Absolute Values Algebraically ("By Cases")
  23. 23 Factorising Non-Monic Quadratics: 4 Methods
  24. 24 The difference between “And” & “Or”
  25. 25 Linear Functions (1 of 2: Simple Forms)
  26. 26 Linear Functions (2 of 2: Forms Involving Geometric Features)
  27. 27 Functions & Relations (1 of 2: Introductory Concepts)
  28. 28 Functions & Relations (2 of 2: Vertical Line Test)
  29. 29 Ways to Write Domain (& Range)
  30. 30 Modifying Graphs by Shift, Reflection & Stretch
  31. 31 Completing the Square (1 of 2: Simple Numerical Example)
  32. 32 Completing the Square (2 of 2: The Quadratic Formula)
  33. 33 The Pieces of a Parabola
  34. 34 Vertex Form of a Parabola (1 of 2: Why it matters)
  35. 35 Vertex Form of a Parabola (2 of 2: Inductive Derivation)
  36. 36 Quadratic Functions: What the Discrimant tells you
  37. 37 Definite & Indefinite Quadratics (1 of 3: The Right Conditions)
  38. 38 Definite & Indefinite Quadratics (2 of 3: Example Questions)
  39. 39 Definite & Indefinite Quadratics (3 of 3: Working the Inequalities)
  40. 40 Deriving the Quadratic Formula
  41. 41 Introduction to Functions (1 of 2: Basic Idea & Formal Definition)
  42. 42 Introduction to Functions (2 of 2: Examples & Counter-Examples)
  43. 43 Domain & Range (1 of 2: Definitions)
  44. 44 Working with Functions (1 of 2: Notation & Terminology)
  45. 45 Working with Functions (2 of 2: Substituting Variables)
  46. 46 Domain & Range (2 of 2: Introductory Examples)
  47. 47 5.3 Functions - Evaluating Expressions with Function Notation
  48. 48 Introduction to Absolute Value (1 of 2: Definitions)
  49. 49 Introduction to Absolute Value (2 of 2: Basic Examples)
  50. 50 Graphing Absolute Value Functions (1 of 2: y = 2(x+1) - |x+1|)
  51. 51 Graphing Absolute Value Functions (2 of 2: y = |x+1| - |x-2|)
  52. 52 Absolute Value - Solve |x-1| = |½x+1| (1 of 2: Constructing Graphs)
  53. 53 Absolute Value - Solve |x-1| = |½x+1| (2 of 2: Interpreting Graphs)
  54. 54 Equations of Straight Lines (1 of 2: Slope-Intercept Form)
  55. 55 Equations of Straight Lines (2 of 2: General Form)
  56. 56 Intro to Real Functions (1 of 4: Relations)
  57. 57 Intro to Real Functions (2 of 4: Domain & range)
  58. 58 Intro to Real Functions (3 of 4: Characteristics of a function)
  59. 59 Intro to Real Functions (4 of 4: Testing & restricting functions)
  60. 60 Identifying Domain & Range for Unusual Graphs
  61. 61 Odd & Even Functions (1 of 2: Understanding initial examples)
  62. 62 Odd & Even Functions (2 of 2: Formal algebraic definitions)
  63. 63 Definite & Indefinite Quadratics (1 of 2: Using the discriminant)
  64. 64 Definite & Indefinite Quadratics (2 of 2: Example questions)
  65. 65 Finding the Domain of a Given Radical Function
  66. 66 Using the Discriminant (Exam question about points of intersection)
  67. 67 Solving Absolute Value Equation Example 3x + 2 = |2x - 1|
  68. 68 Quadratic Factorisation (1 of 3: Overview of Methods)
  69. 69 Quadratic Factorisation (2 of 3: Translating to a quadratic equation)
  70. 70 Quadratic Factorisation (3 of 3: Interpreting quadratic solutions)
  71. 71 Algebraic Fractions (1 of 3: Why do they matter?)
  72. 72 Algebraic Fractions (2 of 3: Example questions)
  73. 73 Algebraic Fractions (3 of 3: Denominators & restricted domains)
  74. 74 Problem Solving with Quadratic Equations (1 of 2: Geometry example)
  75. 75 Problem Solving with Quadratic Equations (2 of 2: Watching for restrictions)
  76. 76 Simultaneous Equations (1 of 2: By elimination)
  77. 77 Simultaneous Equations (2 of 2: By substitution)
  78. 78 Forming Simultaneous Equations (1 of 2: Fast & Slow Walkers)
  79. 79 Forming Simultaneous Equations (2 of 2: Two Digit Number)
  80. 80 Domain and Range (1 of 2: Introduction)
  81. 81 Domain and Range (2 of 2: Examples)
  82. 82 Classifying Functions & Relations (1 of 2: 1-to-1, Many-to-1)
  83. 83 Classifying Functions & Relations (2 of 2: 1-to-Many, Many-to-Many)
  84. 84 Interval Notation (1 of 2: Bounded intervals)
  85. 85 Interval Notation (2 of 2: Unbounded intervals)
  86. 86 Graphing Quadratics Equations (1 of 6: Why do we care about them?)
  87. 87 Graphing Quadratics Equations (2 of 6: Summary of basic features)
  88. 88 Graphing Quadratics Equations (3 of 6: x & y-intercepts)
  89. 89 Graphing Quadratics Equations (4 of 6: Visually interpreting background calculations)
  90. 90 Graphing Quadratics Equations (5 of 6: Considering accuracy & rounding)
  91. 91 Graphing Quadratics Equations (6 of 6: Locating the vertex)
  92. 92 Graphing Parabolas via Transformation (1 of 2: Rearranging algebraically)
  93. 93 Graphing Parabolas via Transformation (2 of 2: Thinking visually)
  94. 94 Graphing Cubic Functions (1 of 4: Considering y = x³)
  95. 95 Graphing Cubic Functions (2 of 4: Vertical translation)
  96. 96 Graphing Cubic Functions (3 of 4: Factored form)
  97. 97 Graphing Cubic Functions (4 of 4: Geometric features)
  98. 98 Simultaneous Linear/Quadratic Equations (1 of 2: Considering a line & parabola)
  99. 99 Simultaneous Linear/Quadratic Equations (2 of 2: Varying numbers of solutions)
  100. 100 Graphing Circles (1 of 4: Review of functions)
  101. 101 Graphing Circles (2 of 4: Centering on the origin)
  102. 102 Graphing Circles (3 of 4: Other centres/radii)
  103. 103 Graphing Circles (4 of 4: Completing the square)
  104. 104 Equation of a Semicircle
  105. 105 Absolute Value Equations & Inequalities (1 of 4: Visualising an equation)
  106. 106 Absolute Value Equations & Inequalities (2 of 4: Visualising the inequality)
  107. 107 Absolute Value Equations & Inequalities (3 of 4: Separate intervals)
  108. 108 Absolute Value Equations & Inequalities (4 of 4: Graphing to avoid unnecessary algebra)
  109. 109 Reflecting Functions (1 of 3: Setting up an example)
  110. 110 Reflecting Functions (2 of 3: What happens when we graph f(-x)?)
  111. 111 Reflecting Functions (3 of 3: What happens when we graph -f(x)?)
  112. 112 Function Symmetry (1 of 4: Overview & definitions)
  113. 113 Function Symmetry (2 of 4: Why are they called "odd" & "even"?)
  114. 114 Function Symmetry (3 of 4: Combining symmetries)
  115. 115 Function Symmetry (4 of 4: Differentiating an odd function)
  116. 116 Introduction to Functions

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