Guide to Parent Functions

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By
Jennifer Ledwith
Jennifer Ledwith
Math Expert
  • B.B.A., Finance and Economics, University of Oklahoma
Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics.
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Updated on November 17, 2019

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
of 09

Types of Functions

02
of 09

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
of 09

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
of 09

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
of 09

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
of 09

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
of 09

Sine Parent Function

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

Cosine Parent Function

  • Equation: y = cosx
  • Domain: All real numbers
  • Range: All real numbers between -1 and 1 (-1≤ y ≤ 1)
09
of 09

Tangent Parent Function

  • Equation: y = tanx
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Your Citation
Ledwith, Jennifer. "Guide to Parent Functions." ThoughtCo, Aug. 27, 2020, thoughtco.com/guide-to-parent-functions-2312307. Ledwith, Jennifer. (2020, August 27). Guide to Parent Functions. Retrieved from https://www.thoughtco.com/guide-to-parent-functions-2312307 Ledwith, Jennifer. "Guide to Parent Functions." ThoughtCo. https://www.thoughtco.com/guide-to-parent-functions-2312307 (accessed April 2, 2023).