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