Exponential functions

An exponential function is one of the form

where \(b\in\mathbb{R}\) (called the ‘base’ of the function) is a constant, \(b\gt 0\) and \(b\neq 1\). We disallow \(b=0\) and \(b=1\) because the function would then be a constant function. We disallow \(b\lt 0\) because it would result in infinite discontinuities in the domain of the function.