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.