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- Parent_function abstract "In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general formthe simplest function is.This is therefore the parent function of the family of quadratic equations.For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes. For example, the graph of y = x2 − 4x + 7 can be obtained from the graph of y = x2 by translating +2 units along the X axis and +3 units along Y axis. This is because the equation can also be written as y − 3 = (x − 2)2.For many trigonometric functions, the parent function is usually a basic sin(x), cos(x), or tan(x). For example, the graph of y = A sin(x) + B cos(x) can be obtained from the graph of y = sin(x) by translating it through an angle α along the positive X axis (where tan(α) = A⁄B), then stretching it parallel to the Y axis using a stretch factor R, where R2 = A2 + B2. This is because A sin(x) + B cos(x) can be written as R sin(x−α) (see List of trigonometric identities).The concept of parent function is less clear for polynomials of higher power because of the extra turning points, but for the family of n-degree polynomial functions for any given n, the parent function is sometimes taken as xn, or, to simplify further, x2 when n is even and x3 for odd n. Turning points may be established by differentiation to provide more detail of the graph.".
- Parent_function wikiPageExternalLink parent-function-definition.
- Parent_function wikiPageID "38912269".
- Parent_function wikiPageRevisionID "594902857".
- Parent_function date "March 2013".
- Parent_function hasPhotoCollection Parent_function.
- Parent_function reason "The definition is not precise, and lacks authoritative references".
- Parent_function talk "Ambiguous definition".
- Parent_function subject Category:Curves.
- Parent_function subject Category:Elementary_algebra.
- Parent_function subject Category:Functions_and_mappings.
- Parent_function comment "In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general formthe simplest function is.This is therefore the parent function of the family of quadratic equations.For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes.".
- Parent_function label "Parent function".
- Parent_function sameAs m.0s8x2dm.
- Parent_function sameAs Q17078119.
- Parent_function sameAs Q17078119.
- Parent_function wasDerivedFrom Parent_function?oldid=594902857.
- Parent_function isPrimaryTopicOf Parent_function.