Answer
The graph is shown below.
Work Step by Step
$xy=1$
Divide x on both sides: $xy=1$,
$\begin{align}
& \frac{xy}{x}=\frac{1}{x} \\
& y=\frac{1}{x}
\end{align}$
Now substitute $x=-4$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{-4} \\
& =-\frac{1}{4} \\
& =-0.25
\end{align}$
Now substitute $x=-3$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{-3} \\
& =-\frac{1}{3} \\
& =-0.33
\end{align}$
Now substitute $x=-2$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{-2} \\
& =-\frac{1}{2} \\
& =-0.5
\end{align}$
Now substitute $x=-1$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{-1} \\
& =-\frac{1}{1} \\
& =-1
\end{align}$
Now substitute $x=1$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{1} \\
& =1
\end{align}$
Now substitute $x=2$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{2} \\
& =0.5
\end{align}$
Now substitute $x=3$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{3} \\
& =0.33
\end{align}$
Now substitute $x=4$ into the equation $y=\frac{1}{x}$,
$\begin{align}
& y=\frac{1}{4} \\
& =0.25
\end{align}$
Therefore, the required table is,
$\begin{matrix}
x & -4 & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\
y=\frac{1}{x} & -0.25 & -0.33 & -0.5 & -1 & 1 & 0.5 & 0.33 & 0.25 \\
\end{matrix}$
Now plot the points and draw two curves.
