## Algebra## Exponents and Logarithms |

## What is an exponential function? |

Along with exponents come exponential functions, or the relationship between values of a variable and the numbers formed by raising some positive number to the power of those values. In functional notation, an exponential function is written *f*(*x*) = *a*^{x}, in which *a* is a positive number; for example, the function *f*(*x*) = 2^{x} is an exponential function.

In logarithmic terms, an exponential function is most commonly written as exp (*x)* or *e ^{x},* in which

*e*is called the base of the natural logarithm. These types of functions are usually shown on a graph. (For more information about graphs, see “Geometry and Trigonometry.”) As a function of the real variable

*x*, the resulting graph of

*e*is always positive, or above the

^{x}*x*axis and increasing from left to right. Although the line of such a function never touches the

*x*axis, it gets very close to it.