# Is xy = 7  a function?

Aug 4, 2015

If $x$ and $y$ are related by $x y = 7$, the $y$ is a function of $x$.

#### Explanation:

Solve the equation for $y$.

We get $y = \frac{7}{x}$

Now ask yourself: If I choose an $x$, do I ever get two different numbers for $y$? If the answer is NO, the $y$ is a function of $x$.

In this case the answer IS no, so, $y$ is a function of $x$.

For comparison

If $x$ and $y$ are related by $x + {y}^{2} = 3$, then $y$ is NOT a function of $x$.

When we solve for $y$, we get:

${y}^{2} = 3 - x \text{ }$ so

$y = \pm \sqrt{3 - x}$

Now, if I put in a number for $x$, I (usually) get TWO numbers for $y$. (except when $x = 3$).
But if I EVER get two numbers (even just for one single solitary $x$) then $y$ is NOT a function ox $x$.

So for $x + {y}^{2} = 3$, we end up with: $y$ is not a function of $x$.