How do you graph and find the discontinuities of #f(x) = 1/x #?

1 Answer
MeneerNask
Aug 17, 2015

The most obvious discontinuity is when #x=0# because that is not defined.

Explanation:

If #x->0# from positive, #f(x)# will grow, or in the "language":
#lim_(x->0^+) f(x)=oo#

Almost he same goes for #x->0# from negative:
#lim_(x->0^-) f(x)=-oo#

If #x# gets greater and greater (both positive and negative) #f(x)# will be smaller and smaller, without actually reaching #0#, or:
#lim_(x->oo) f(x)=lim_(x->-oo) f(x)=0#

#x=0 and y=0# are called the asymptotes.
graph{1/x [-10, 10, -5, 5]}

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