Checking if Continuous Over an Interval

Another person might write the introduction to Checking if Continuous Over an Interval as follows: To verify whether a function is continuous over a designated interval, it is necessary to confirm that the function is not only defined and finite but also smooth across the entire interval. This means there shouldn't be any interruptions, leaps, or gaps in the function. Essentially, the limit of the function from both directions at any given point in the interval should equate to the actual value of the function.