# How do you find the domain of y = 3/x?

$x \ne 0$

#### Explanation:

The Domain is the list of allowable values of $x$. I find it easiest to first say $x$ is all values and then find any that $x$ can't be. So - are there any values that $x$ can't be?

The answer is yes: $x \ne 0$ because that would make the fraction divisible by 0 and that is a no-no.

We can express this in a few different ways. One way is to simply write $x \ne 0$. Another is to write $\left(- \infty , 0\right) , \left(0 , \infty\right)$. And there are others that have more rigorous notation.

Here's a graph to see the disallowed value of $x$:

graph{3/x[-10,10,-100,100]}