Functions

Exponential Function

Function defined by a relation in the form f(x) = [latex]{a}^{x}[/latex] where a is a strictly positive real number that is different from 1.
  • The graph of an exponential function passes through the point (0, 1), no matter what the base of the function is.
  • The functions defined by f(x) = [latex]{a}^{x}[/latex] and g(x) = [latex]\log{(ax)}[/latex] are the inverse of one another.
  • If a > 1, the function defined by the relation f(x) = [latex]{a}^{x}[/latex] is increasing in [latex]\mathbb{R}[/latex] and if 0 < a < 1, it is decreasing in [latex]\mathbb{R}[/latex].

Example

The function f defined in the set of real numbers by the relation f(x) = [latex]{2}^{x}[/latex] is an exponential function with base 2.

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