Question

What are the intervals in which the function is continuous

y=3/((x+2)^2+4)

Answer 1

The function is continuous only on its domain. We have to check if there are any values of x where y does not exist for the given y. The usual culprits of discontinuities are even indexed radicals (cannot have negatives under radical) and fractions with variables in the denominator (variable cannot cause a denominator=0 situation).

We can see the denominator does have a variable in its denominator, so we have to check for when it equals 0.

(x + 2)^2 + 4 = 0
(x + 2)^2 = -4
x + 2 = sqrt(-4) <<Not a real number.

Thus, there isn't any place on y where the function 'disappears.'

(-infinty, infinity) or -infinty < x < infinity
> interval notation or inequality