Guide to Parent Functions

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Guide to Parent Functions

The modern dating game is a staple of reality TV. For the Love of Ray J, Flavor of Love, and The Bachelorette all descend from the same daddy: The Bachelor. Although some of The Bachelor's derivative shows differ, they all take cues from The Bachelor.

Dating Show Characteristics

  • 1 attractive person for several potential suitors
  • The show will conclude with matching true loves
  • Backbiting is involved

Similarly, each family of Algebraic functions is headed by a parent.

Types of Functions

  • Linear
  • Quadratic
  • Absolute Value
  • Exponential Growth
  • Exponential Decay
  • Trigonometric (Sine, Cosine, Tangent)
  • Rational
  • Exponential
  • Square Root

Each of these functions has a parent function. This article focuses on the traits of the parent functions.

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Linear Parent Function

  • Equation: y = x
  • Domain: All real numbers
  • Range: All real numbers
  • Slope of the line: m = 1
  • y-intercept: (0,0)

Additional Information about Linear Functions

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Quadratic Parent Function

  • Equation: y = x2
  • Domain: All real numbers
  • Range: All real numbers greater than or equal to 0. (y ≥ 0)
  • y-intercept: (0,0)
  • x-intercept: (0,0)
  • Line of symmetry: (x = 0)
  • Vertex: (0,0)

Additional Information about Quadratic Functions

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Absolute Value Parent Function

  • Equation: y = |x|
  • Domain: All real numbers
  • Range: All real numbers greater than or equal to 0. (y ≥ 0)
  • y-intercept: (0,0)
  • x-intercept: (0,0)
  • Line of symmetry: (x = 0)
  • Vertex: (0,0)

Additional Information about Absolute Value Functions

Definition of Absolute Value

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Exponential Growth Parent Function

  • Equation: y = bx(where |b| > 0)
  • Domain: All real numbers
  • Range: All real numbers greater than or equal to 0. (y ≥ 0)
  • y-intercept: (0,1)

Additional Information about Exponential Growth Functions

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Exponential Decay Parent Function

  • Equation: y = bx(where 0
  • Domain: All real numbers
  • Range: All real numbers greater than or equal to 0. (y ≥ 0)
  • y-intercept: (0,1)

Additional Information about Exponential Decay Functions

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Sine Parent Function

  • Equation: y = sinx
  • Domain: All real numbers
  • Range: All real numbers between -1 and 1 (-1≤  y ≤ 1)

Additional Information about Sine Functions

Finding Sine

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Cosine Parent Function

  • Equation: y = cosx
  • Domain: All real numbers
  • Range: All real numbers between -1 and 1 (-1≤  y ≤ 1)

Additional Information about Cosine Functions

Finding Cosine

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Tangent Parent Function

  • Equation: y = tanx