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

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Answer 1 · 2015-11-05T10:38:47

Function means: at most one $y$ for every $x$

We can rewrite as $y=9/x$ or even $x=9/y$

In both cases we get only one answer, except when $x=0$ or $y=0$
so we can say: $y=f(x)$ and $x=g(y)$
graph{9/x [-22.8, 22.83, -11.4, 11.4]}

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