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