How do you explain to a student who is struggling with math that 1/x gets arbitrarily large as x goes to 0?

In doing online tutoring, I have run into students who just don’t see it. Usually it is for a graphing problem like y = 2/(1 – x). They have no trouble seeing that y goes to zero as x gets large.

Is there some way of making this intuitive? To me it seems so obvious. What I usually do is point out that ½ goes into 1 twice and 1/100 goes into 1 a hundred times, and so on, but this approach has not been very successful.