Exponential functions are characterized by a particular pattern in which the rate of change of any mathematical function is proportional to the current value of the function. An exponential function may present itself as either of two possibilities. The first is exponential growth, which shows a growth rate of a given function in proportion to the function's value. The second is exponential decay, which posts a negative growth rate.

The most widely-known exponential parent function involves Euler's number e and follows the formula y = e^x. This function produces an exponential graph that slopes upward and becomes steeper as the value of x increases. The gradually steeper curve is produced because of the geometric progression that the function is following.

Parent functions exist for practically every type of algebraic function. The simplest parent function is y = x, which presents a direct proportionality between the dependent variable y and the independent variable x.