If they are equal the function is continuous at that point and if they aren't equal the function isn't continuous at that point. ... The function value and the limit aren't the same and so the function is not continuous at this point. This kind of discontinuity in a graph is called a jump discontinuity.
What makes not continuous?
In other words, a function is continuous if its graph has no holes or breaks in it. For many functions it's easy to determine where it won't be continuous. Functions won't be continuous where we have things like division by zero or logarithms of zero.
How do you know if something is not continuous?
How to Determine Whether a Function Is Continuous or...
- f(c) must be defined. ...
- The limit of the function as x approaches the value c must exist. ...
- The function's value at c and the limit as x approaches c must be the same.
