Answer
The graph is shown below.
Work Step by Step
$f\left( x \right)={{\log }_{6}}x$
Assume, $f\left( x \right)=y$
Therefore, the function becomes, $y={{\log }_{6}}x$
Therefore, the function $y=f\left( x \right)={{\log }_{6}}x$ can be written as $x={{6}^{y}}$
Substitute $y=0,1,2,-1,-2$ in the function ${{6}^{y}}=x$ and tabulate the values as shown in Table 1.
$\begin{align}
& x={{6}^{0}} \\
& =1
\end{align}$
$\begin{align}
& x={{6}^{1}} \\
& =6
\end{align}$
$\begin{align}
& x={{6}^{2}} \\
& =36
\end{align}$
$\begin{align}
& x={{6}^{-1}} \\
& =\frac{1}{6}
\end{align}$
$\begin{align}
& x={{6}^{-2}} \\
& =\frac{1}{36}
\end{align}$
Tabulate the obtained values as shown below:
$\begin{matrix}
x & y \\
1 & 0 \\
6 & 1 \\
36 & 2 \\
\frac{1}{6} & -1 \\
\frac{1}{36} & -2 \\
\end{matrix}$
