How do you find the intervals on which the function is continuous given #y = (2)/((x + 4)^2) + 8#?

1 Answer
Feb 23, 2018

Answer:

The function is continuous at all points except where x=-4. The domain of the function can be given by.
#(-oo, -4)uu(-4, oo)#

Explanation:

The given function is defined only for the points where denominator i.e. #(x+4)^2# is not equal to zero.

the only point on the real number line where the given function is not defined is at #x=-4#.

Hence, its interval is given by #(-oo, -4)uu(-4,oo)#. graph{(2)/((x+4)^(2))+8 [-10, 10, -5, 5]} graph{(2)/((x+4)^(2))+8 [-24.85, 16.47, 1.22, 21.87]}

Edit: Move the graph to view the horizontal asymptote at #y=8^+#.