Graphing Rational Functions

Let's graph the function by ourselves to determine the error and correct it. $$\begin{array}{c}y=\frac{\text{-}8}{x}\end{array}$$ The function is in the form of $y=\frac{a}{x},$ so the asymptotes are $x=0$ and $y=0.$ Knowing the asymptotes, we will make a table of values for the given function.

$x$	$\frac{\text{-}8}{x}$	$y$
$\text{-}4$	$\frac{\text{-}8}{\text{-}4}$	$2$
$\text{-}2$	$\frac{\text{-}8}{\text{-}2}$	$4$
$\text{-}1$	$\frac{\text{-}8}{\text{-}1}$	$8$
$0$	$\frac{\text{-}8}{0}$	Asymptote
$1$	$\frac{\text{-}8}{1}$	$\text{-}8$
$2$	$\frac{\text{-}8}{2}$	$\text{-}4$
$4$	$\frac{\text{-}8}{4}$	$\text{-}2$

Next, we will plot the points and draw two branches of the hyperbola so that they pass through the plotted points and approaches the asymptotes.

Therefore, we can say that the branches of the hyperbola are in the wrong quadrants.