Well it begs the question - is it really an asymptote?
When you substitute Y=1 into the formula, you get X=0.
I wrote this in my book:
When x>0, y(cannot equal)1
When x<0, y(cannot equal)1
When x=0, y=0
Then drew the graph, but didn't mark y=1 as an asymptote as the line travels through it.