Question

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

Answer 1

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^+`.