2.23 Graphs of the exponential functions

We define $e^{x}=\exp(x)=\exp x$ to be the exponential function; in view of (i), (ii) and (iii), this matches with the standard notation for powers (exponents). Hence we have

Confusingly, $e^{-x}$ is sometimes called a negative exponential function; ‘negative’ refers to the coefficient of $x$ and not to the sign of the function.