Answer
The graph is shown below.
Work Step by Step
$f\left( x \right)={{\log }_{4}}x$
Assume, $f\left( x \right)=y$
Therefore, the function becomes $y={{\log }_{4}}x$
The function $y={{\log }_{4}}x$ can be written as $x={{4}^{y}}$.
Substitute in a selected y value:
$\begin{align}
& x={{4}^{0}} \\
& =1
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{4}^{1}} \\
& =4
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{4}^{2}} \\
& =16
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{4}^{-1}} \\
& =\frac{1}{4}
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{4}^{-2}} \\
& =\frac{1}{16}
\end{align}$
Tabulate the obtained values as shown below:
$\begin{matrix}
{{4}^{y}}=x & y \\
1 & 0 \\
4 & 1 \\
16 & 2 \\
\frac{1}{4} & -1 \\
\frac{1}{16} &-2 \\
\end{matrix}$
