Answer
$f(x)=\log_{4}x$
Work Step by Step
Create a table of function values.
For x, select powers of $4$, since $\log_{4}4^{n}=n$
$\left[\begin{array}{lllllll}
x & 1/16 & 1/4 & 1 & 2 & 4 & 16\\
f(x) & -2 & 1 & 0 & 1/2 & 1 & 2
\end{array}\right]$
Plot the points and join with a smooth curve.