Danielle P.

# how do i find where a function is discontinuous if the bottom part of the function has been factored out?

Indicate all values for which the function is discontinuous. for each discontinuity point "a" give the limit of the function as x approaches "a". Clearly indicate limits that do not exist.

f(x)= ((x^2)-4)/((x-2)(x+3))

would the funciton be discontinuous at x=2 and x=-3; and would the limits not exist? I am confused..

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Helga M.

I believe you mistyped. The limit exists at x = 2, not x=-2. :-)

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10/01/12

Michael B.

Helga, actually the limit DOES exist at -2, but it is a trivial answer because you can simply plug -2 into the function - the answer is 0 of course.  In other words, there's nothing special happening at x=-2 - no holes, no asymptotes, etc.  I think that's what you meant, but wanted to make sure it doesn't confuse people.

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11/14/12

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