Answer
The graph is shown below.
Work Step by Step
$f\left( x \right)={{\log }_{2.5}}x$
Assume, $f\left( x \right)=y$
Therefore, the function becomes: $y={{\log }_{2.5}}x$
Therefore, the function $y={{\log }_{2.5}}x$ can be written as $x={{2.5}^{y}}$
Substitute $y=0,1,2,-1,-2$ in the function ${{2.5}^{y}}=x$ and tabulate the values as shown in Table 1.
Substitute in a selected y value:
$\begin{align}
& x={{\left( 2.5 \right)}^{0}} \\
& =1
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{\left( 2.5 \right)}^{1}} \\
& =2.5
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{\left( 2.5 \right)}^{2}} \\
& =6.25
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{\left( 2.5 \right)}^{-1}} \\
& =\frac{1}{2.5}
\end{align}$
Substitute in a selected y value:
$\begin{align}
& x={{\left( 2.5 \right)}^{-2}} \\
& =\frac{1}{{{2.5}^{2}}} \\
& =\frac{1}{6.25}
\end{align}$
Tabulate the obtained values as shown below:
$\begin{matrix}
{{2.5}^{y}}=x & y \\
1 & 0 \\
2.5 & 1 \\
6.25 & 2 \\
0.4 & -1 \\
0.16 & -2 \\
\end{matrix}$
