Question

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

Answer 1

`x!=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!=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!=0`. Another is to write `(-oo,0), (0,oo)`. 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]}