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

1 Answer
Feb 23, 2018

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^+.