Question

Under what conditions can you extend a function f(x) to be continuous at a point x=c?

Is this just rules for continuity or am I just really confused? If not what is this question asking?

Answer 1

Yes, rules of continuity. Has to have same limits from left and right, and has to be differentiable at that point.

Answer 2

Yes, use the definition of continuity. So, the limit of x to c has to exist. You can then define value of the function at x = c to be equal to that limit.