Intermediate Algebra, Chapter 3, 3.5, Section 3.5, Problem 56

Identify whether the relation $xy = 3$ defines $y$ as the function of $x$ and give the domain.

First, we solve $y$ by dividing both sides by $x$, So we have
$\displaystyle y = \frac{3}{x}$
Given any value of $x$, we find $y$ by dividing $3$ into $x$.
This process produces exactly one value of $y$ for each value in the domain, so the given equation defines a function.
The domain includes all real numbers except those which value the denominator . We find these numbers by setting the
denominator equal to and solving for $x$. In this case,

$\begin{equation} \begin{aligned} x = 0 \end{aligned} \end{equation}$

The domain includes all real numbers except , written $(-\infty, 0) \bigcup (0, \infty)$