Exponential Function

Exponential Function

Function defined by a relation in the form f(x) = \({a}^{x}\) 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) = \({a}^{x}\) and g(x) = \(\log{(ax)}\) are the inverse of one another.
  • If > 1, the function defined by the relation f(x) = \({a}^{x}\) is increasing in \(\mathbb{R}\) and if 0 < a < 1, it is decreasing in \(\mathbb{R}\).


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

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