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~

Answer 1

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