Guide to Parent Functions

Teenage Girl Sits Smiling at a Desk in Front of a Blackboard
Teenage Girl Sits Smiling at a Desk in Front of a Blackboard. Digital Vision/Getty Images

The modern dating game is a staple of reality TV. "The Bachelorette" and "Flavor of Love," for example, both descended from the same parent: "The Bachelor." Although these shows may differ slightly from "The Bachelor," they still share major characteristics with the parent show:

  • There is one 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, as described in the following sections, including example equations.

01
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Types of Functions

02
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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)
03
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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)
  • S-intercept: (0,0)
  • Line of symmetry: (x = 0)
  • Vertex: (0,0)
04
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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)
05
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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)

06
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Exponential Decay Parent Function

  • Equation: y = bx
  • Domain: All real numbers
  • Range: All real numbers greater than or equal to 0. (y ≥ 0)
  • Y-intercept: (0,1)
07
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Sine Parent Function

  • Equation: y = sin
  • Domain: All real numbers
  • Range: All real numbers between -1 and 1 (-1≤ y ≤ 1)
08
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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)
09
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Tangent Parent Function

  • Equation: y = tanx