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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