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Continuity Proof

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Let f: R-> R be a function that satisfies f(x+y) = f(x) + f(y) for all x,y in R.

Suppose that f is continuous at some point c. Prove that f is continuous on R.

How would you go about starting this proof??

I do not understand the f(x+y) = f(x)+f(y) thing.

Does some point c make f continuous on R??

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A continuity proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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Proof:
First, f(x) is continuous at c, this means for any e>0, we can find some d>0, such that for
all x with |x-c|<d, we have |f(x)-f(c)|<e.
More over, for all x with |x-c|<d, we can assume that ...

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