Why is it impossible to have lim_(x->0) f(x) and lim_(f(x)->0)f(x) simultaneously exist for any of these graphs?
A) f(x) = 1/x^2
B) f(x) = -1/x^2
C) f(x) = 1/x
D) f(x) = -1/x
2 Answers
All four of these graphs have the
Well, by definition, a vertical asymptote is when at
For the function
y = c/x ,
where
But if you have
(Imagine trying to run to two different places at once; can't do it.)
Both kinds of asymptotes are on the graph, to be sure, but you can only approach one of those kinds of asymptotes at a time.