Describe the intervals on which the following function is continuous. If not continuous, state "where" the discontinuity occurs and state the TYPE of discontinuity.

Question

Describe the intervals on which the following function is continuous. If not continuous, state "where" the discontinuity occurs and state the TYPE of discontinuity.
f(x)= (x^2-x-12)/(x^2-6x+8)

I just don't understand how to find the intervals. Thanks~

Reiny · Answer

f(x)= (x^2-x-12)/(x^2-6x+8)
= (x-4)(x+3)/( (x-2)(x-4)
= (x+3)/(x-2) , x not= 4

So the function is discontinuous at x=4 and at x = 2
with a "hole" at (4, 7/2)
and a vertical asymptote at x = 2

So continuous for

x<2 OR x > 2, x not= 4