is it always true that if the limit of a function as x approaches 4 exist, that f(4) is defined? Explain & provide a equation and graph.

1 Answer

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nathanshields | High School Teacher | (Level 1) Associate Educator

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Think about the function `f(x)=(x-4)/(x-4)` .

If you put in any number except 4, the function returns 1.  But if you put in 4, you get 0/0, which is undefined.  Since the limit as x approaches 4 never involves x=4, we have `lim_(x->4)f(x)=1` but ``f(4) is undefined.