Answer
It is a function
Domain = $(–\infty, 0)$ $\cup$ $(0, \infty)$
Range = $(–\infty, 0)$ $\cup$ $(0, \infty)$
Work Step by Step
Refer to the curve $xy = 2$ in Graph I, it is a function because
by way of Vertical Line Test, each vertical line drawn will not intersect the curve on the graph in more than one point, so, the equation defines a function.
For $xy = 2$, one corresponding value of y can always be found for any choice of x in the domain of $(–\infty, 0)$ $\cup$ $(0, \infty)$.
y will be any real number with range $(–\infty, 0)$ $\cup$ $(0, \infty)$.
