# 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 $$\mathbb{R}$$.

### 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.