How do you decide whether the relation $xy+7y=7$ defines a function?

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Answer 1 · 2015-11-09T05:00:25

You can rearrange the expression to find that $y$ is uniquely determined in terms of $x$ , therefore a function.

$7 = xy + 7y = (x+7)y$

Notice that if $x = -7$ then there are no solutions, since this results in $7 = 0y = 0$ .

If $x != -7$ then we can divide both sides by $x+7$ to get:

$7/(x+7) = y$

That is:

$y = 7/(x+7)$

This uniquely determines the value of $y$ for any value of $x$ apart from $x=-7$ , where it is not defined.

How do you decide whether the relation xy+7y=7xy+7y=7 defines a function?