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

We can factor the denominator and then use the Definition of Continuity:

. We see that except at x = 3, . For a solution at points other than x = 3, see the related problem.

When x = 3, we cannot cancel and we must work with the original function.

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

Does the function have a limit at the same point? Since the one-sided limits do not involve the point, we can still cancel: we need

Since these limits are equal, the limit exists at x = 3.

Can the discontinuity be removed? Yes, the function can be separately defined to equal its limit, making the discontinuity removable.