Answer
True.
Work Step by Step
All graphs of $f(x)=a^{x}$ have the $x$-axis as the horizontal asymptote.
If $f(x)=a^{x}$, with $a\gt 0$ and $a\neq 1$,
the domain of $f$ is all real numbers, and
the range of $f$ is all positive real numbers, $(0, \infty)$.
$ e \gt 0, \quad e\neq 1.$ so the statement is true.
