Is the Function f(x) = 2x + 3 Continuous Over All Real Numbers?

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Give a formal proof that the function , f(x) = 2x + 3 is continuous over the real Nos R
 
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Why?
 
What is the definition of "continuous on a set"? That is a good place to start.

Hurkyl is saying "It's your question- you go first!"
 

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