Determine whether this function is continuous at x = 3. If it is discontinuous, is the discontinuity removable?

We can use the Definition of Continuity:

Is the function defined at x = 3? Yes, it is defined as 1 - x = 1 - 3 = -2 there.

Does the function have a limit at the same point? Yes: see the related problem.

Is the function continuous? Since the limit, -2, and the value at x = 3 are the same, the Definition tells us that the function is continuous.