# 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?

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#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.