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Parent Function


A parent function is a simple representative of a family of related functions. Other members of the family are obtained from it by transformations such as translations, reflections, stretches, and compressions of its function graph. For example, f(x)=x is commonly used as the parent for linear functions, f(x)=x^2 for functions represented by quadratic polynomials, and f(x)=|x| for absolute-value functions.

The choice of parent is a convention for organizing related graphs rather than an intrinsic property of a function.


See also

Absolute Value, Function, Function Graph, Linear Function, Quadratic Polynomial, Reflection, Translation

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References

Abramson, J. "Transformation of Functions." §1.5 in Precalculus. Houston, TX: OpenStax, 2014. https://openstax.org/books/precalculus/pages/1-5-transformation-of-functions.

Cite this as:

Weisstein, Eric W. "Parent Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParentFunction.html

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