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?

2 answers

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