Find the dicontinuities of the function. f(x) =
x2 + 12x + 27
x2 + 4x + 3
.
There is a removable discontinuity at
(
,
).

Step-by-step explanation:

I'm assuming you meant to type in

because you can only have removable discontinuities where there is a rational (fraction) function. Begin by factoring both the numerator and denominator to

and cancelling out like terms would have us eliminating the (x + 3). That is where there is a removable discontinuity. It leaves a hole. The other discontinuity, (x + 1) doesn't cancel out so it is a non-removable discontuinity, which is a vertical asymptote.

The removable discontinuity is at -3. There is no y value at x = -3 (remember there's only a hole here), because -3 causes the denominator to go to 0 and we all know that having a 0 in the denominator of a fraction is a big no-no!!!