Exponential function

The exponential function is one of the most important functions in mathematics. It is written as exp(x) or ex, where e is the base of the natural logarithm.

Related Topics:
Function - Mathematics - Base of the natural logarithm

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As a function of the real variable x, the graph of ex is always positive (above the x axis) and increasing (viewed left-to-right). It never touches the x axis, although it gets arbitrarily close to it (thus, the x axis is a horizontal asymptote to the graph). Its inverse function, the natural logarithm, ln(x), is defined for all positive x.

Related Topics:
Real - Graph - Asymptote - Inverse function - Natural logarithm

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Sometimes, especially in the sciences, the term exponential function is reserved for functions of the form kax,

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where a, called the base, is any positive real number. This article will focus initially on the exponential function with base e.

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In general, the variable x can be any real or complex number, or even an entirely different kind of mathematical object; see the formal definition below.

Related Topics:
Variable - Complex - Formal definition below

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