Question

At what point is this function discontinuous? I thought it was continuous everywhere, but apparently the answer is -2.

Answer 1

being discontinuous at a point does not make the entire function discontinuous

Answer 2

a function is continuous at every point that the limit from the left is equal to the limit from the right.

Answer 3

and discontinuous at the points were the limit from the left is NOT equal to the limit from the right.

Answer 4

Oh, I see. The limit from both sides as x approaches -2 are -1 and 1. They don't match so the limit doesn't exist?

Answer 5

Yes, and because the limit does not exist the function is discontinuous at that point. bear in mind that this does not mean that the entire function is discontinuous,