Answer
$ f(x)=e^{-x}$
Work Step by Step
The graph is above the x-axis, falls from the left to right and passes through (0,1)
$\Rightarrow $ The base is less than 1, no left/right shifts.
It passes through $(1,\displaystyle \frac{1}{e})$, so we assume that the base is $\displaystyle \frac{1}{e},\ f(x)=(\displaystyle \frac{1}{e})^{x}=e^{-x}$
and we check with the other points:
$(\displaystyle \frac{1}{e})^{-1}=e\quad $ ... point $(-1,e)\quad $ ... OK
$(\displaystyle \frac{1}{e})^{-2}=e^{2}\quad $ ... point $(-2,e^{2})\quad $ ... OK
$ f(x)=e^{-x}$
