In mathematics, a parent function is the core representation of a function type without manipulations such as translation and dilation. It is the simplest form of any function family, in which it preserves the definition of the entire family. For example, for the family of quadratic functions having the general form y = ax^2 + bx + c, the simplest function is y = x^2. This is therefore the parent function of the family of quadratic equations.
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 x^n, or, to simplify further, x^2 when n is even and x^3 for odd n.
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 many trigonometric functions, the parent function is usually a basic sin(x), cos(x), or tan(x) .
In summary, a parent function is the most basic function from which a family of similar functions is derived, and it preserves the definition of the entire family.
