Answer
$ f(x)=4^{x}$
Work Step by Step
The graph is above the x-axis, rises from the left to right and passes through (0,1)
$\Rightarrow $ The base is greater than 1, no left/right shifts, no reflections.
It passes through $(1,4)$, so we assume that the base is 4, $ f(x)=4^{x}$, and we check with the other points:
$(4)^{-1}=\displaystyle \frac{1}{4}\quad $ ... point $(-1,\displaystyle \frac{1}{4})\quad $ ... OK
$(4)^{2}=16\quad $ ... point $(2,16)\quad $ ... OK
$ f(x)=4^{x}$
