Continuity - Concept


In order for a function to be continuous at a certain point, three conditions must be met: (1) that the point is in the domain of the function, (2) that the two-sided limit of the function as it approaches the point does in fact exist and (3) the value of the function equals the limit that it approaches. The continuity of a function only exists if these three conditions are met.


I want to talk about a concept called "Continuity," let f of x be a function here is the definition of Continuity.
We say that f of x is continuous at the point x=a if three things are true. First f of a is defined so a has to be in the domain of the function f. Second the limit as x approaches a f of x exists, so the limit has to exist from both sides. And then three the limit as x approaches a of f of x has to equal f of a. So this value in part one has to equal the value in part two. These are the three conditions for Continuity of a function at a point x=a.

limits definition of a function continuous at a point domain of a function