Question

describe the intervals on which f(x) is continuous where f(x)=1/(x-2)^2

Answer 1

Domain of function = (-infinity, 2) U (2, + infinity)
thus

Answer 2

there is an asymptote at 2 and it is continuous from
from (-infinity, 2)
and
from (2, + infinity)

do you understand?

Answer 3

you can't divide by zero so 2 isn't a possible x value you can sub into that function therefore it isn't on your graph so it is a break in the graph. So everything up to that vertical asymptote and to infinity on both sides are continous

Answer 4

thank you so much! and for the explanation as well :)