Question

How do you graph `y =7/x`?

Answer 1

Your function will give you a two part curve looking like the wings of a butterfly!

Explanation:

You first need to determine the `x` values that cannot be accepted by your function. In this case you do not want a division by zero so you need that:
`x!=0`
The `y` axis will then become a VERTICAL asymptote of your function; the graph of your function will get near and near to the `y` axis without ever crossing it.

If you try to get near (but not equal) to zero; you'll see that your function becomes very big (positively or negatively). You express this idea by using the concept of LIMIT:
`lim_(x->0^+)7/x=+oo`
`lim_(x->0^-)7/x=-oo`
This means that when you approximate zero from the right (`0^+`) or the left (`0^-`) the function becomes big (positively or negatively).

On the other hand when `x` becomes very big the function tends to zero (gets very small!!!).
`lim_(x->oo)7/x=0`

So, basically, your graph will look like the wings of a butterfly!!!
graph{7/x [-10, 10, -5, 5]}