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For what values of x, if any, does #f(x) = 1/(x^2-4x+4) # have vertical asymptotes?

Answer 1

#x=2#.

To find the vertical asymptotes we have to find for which values the denominator is equal to 0. Simply set the polynomial on the denominator to 0 then solve for #x#:

#x^2-4x+4=0#
#(x-2)(x-2)=0#
#therefore x = 2#

Thus there is one vertical asymptote at #x=2#.

Here is a graph of the function, the vertical asymptote is clearly indicated by a steep incline towards #x=2#.

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Answer 2

Luke Alvarez

The function f(x) = 1/(x^2-4x+4) has vertical asymptotes at x = 2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.