I am studying continuity presently. This question is related to the terms and phrases used in continuity.
Let $y=f(x)$ denote a real valued function of a real variable. Let $D_f$ be the domain and $C_f$ be the codomain and $R_f$ be the range.
1) What is the difference between the phrases "$f(x)$ is undefined for this value of $x$" and "There is a hole in the graph of $f(x)$ at this point"?
2) What is the difference between the terms "hole", "jump" and "break" used while talking about the graph of a function?