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# 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) = ax, in which a is a positive number; for example, the function f(x) = 2x is an exponential function.

In logarithmic terms, an exponential function is most commonly written as exp (x) or ex, 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 ex is always positive, or above the 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.

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