Posted by Lindsay on Tuesday, August 20, 2013 at 4:45pm.
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^2x12)/(x^26x+8)
I just don't understand how to find the intervals. Thanks~

Math  Reiny, Tuesday, August 20, 2013 at 9:51pm
f(x)= (x^2x12)/(x^26x+8)
= (x4)(x+3)/( (x2)(x4)
= (x+3)/(x2) , 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