Question

What is the vertical asymptote of `y=1/x`?

Answer 1

Well, basically the y axis is the vertical asymptote of this function.
You can see this by trying to get near to it giving values of x near and around the value of zero (which is prohibited!!!)
You'll find that getting near to zero (from the positive or negative side) will give you values of y very big (positively and negatively) as in figure:

The values y of your function will get near and near to the y axis but will never cross it!!!!

You can try by yourself using values of x such as:
0.1
0.01
0.001
or
-0.1
-0.01
-0.001