# How do you decide whether the relation xy=9 defines a function?

Function means: at most one $y$ for every $x$
We can rewrite as $y = \frac{9}{x}$ or even $x = \frac{9}{y}$
In both cases we get only one answer, except when $x = 0$ or $y = 0$
so we can say: $y = f \left(x\right)$ and $x = g \left(y\right)$