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Chapter 1 Fonctions continues

When is a function f continuous?
A function f is continuous when, for every value c in its Domain: If we get different values from left and right (a "jump"), then the limit does not exist! And remember this has to be true for every value c in the domain. Almost the same function, but now it is over an interval that does not include x=1.
How to check the continuity of a function?
From the above definitions, we can define three conditions to check the continuity of the given function. They are: Consider the function f (x) and point x = a. 1. The function must be defined at a point a to be continuous at that point x = a. 2. The limit of the function f (x) should be defined at the point x = a, 3.
Is x=1 a continuous function?
Almost the same function, but now it is over an interval that does not include x=1. So now it is a continuous function (does not include the "hole") But at x=1 you can't say what the limit is, because there are two competing answers: And so the function is not continuous. At x=0 it has a very pointy change!
Is g(x) a continuous function?
In other words g (x) does not include the value x=1, so it is continuous. When a function is continuous within its Domain, it is a continuous function. More Formally ! We can define continuous using Limits (it helps to read that page first): A function f is continuous when, for every value c in its Domain:

When is a function f continuous?