Parent Function
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A parent function is the simplest form of a function in a particular family of functions. It serves as a basic template or reference point from which other functions in the same family are derived by transformations such as translations, reflections, stretching, or shrinking.
For example, here are some common parent functions:
1. Linear Parent Function: f(x) = x
The simplest linear function, a straight line passing through the origin with a slope of 1.
2. Exponential Parent Function: f(x) = 2^x
The simplest exponential function, where the base is a constant (usually 2). It produces a curve that increases rapidly as x increases for positive values and approaches zero as x becomes negative.
3. Quadratic Parent Function: f(x) = x^2
The simplest quadratic function, represented by a parabola that opens upwards with the vertex at the origin.
These parent functions can be transformed to create new functions in the same family by applying changes like shifts, stretches, or reflections.