Determine whether this function is continuous. If it is discontinuous, is the discontinuity removable?

We can use the Definition of Continuity:

Is the function defined at all points? No, it is not defined where the denominator becomes zero, or x = -3. Consequently, the function is discontinuous.

Does the function have a limit at the same point? No.

Can the discontinuity be removed? No because the function does not have a limit at x = -3.