A parent function is the core representation of a function type without manipulations such as translation and dilation. It is the most basic function from which a family of similar functions is derived. For example, the parent function of the family of quadratic functions having the general form y = ax^2 + bx + c is the simplest function y = x^2. Similarly, for many trigonometric functions, the parent function is usually a basic sin(x), cos(x), or tan(x) .

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 = x^2 - 4x + 7 can be obtained from the graph of y = x^2 by translating +2 units along the X axis and +3 units along Y axis.

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.

In summary, a parent function is the simplest form of a function type from which all other functions in that family can be derived by performing various operations like addition, subtraction, multiplication, etc. .