Parent Functions

Parent functions are the basic forms of various families of functions. In short, it represents the simplest form of a function without any transformations. For example, the parent function for the family of linear functions is the function \(y=x\), because any linear function can be derived by applying a transformation (such as shifting or stretching) to this function.

Other examples of common parent functions include:

1. The parent function for the family of quadratic functions is \(y = x^2\)
2. The parent function for the family of cubic functions is \(y = x^3\)
3. The parent function for the family of absolute value functions is \(y = |x|\)
4. The parent function for the family of exponential functions is \(y = b^x\) (where b is a constant greater than 0 and not equal to 1)
5. The parent function for the family of logarithmic functions is \(y = log(x)\) (with base 10 or base e)

Parent functions are used as a starting point to graph and analyze functions within the family. Understanding the parent function can help you understand the behavior and characteristics of all the functions within the family, which can aid in solving problems or analyzing data.