conditions for continuity

Answer 1

For a function to be continuous at a point, three conditions must be met:

1. The function must be defined at the point in question (i.e., the value of x at the point must be in the domain of the function).
2. The limit as x approaches the point from both the left and right must exist.
3. The value of the limit as x approaches the point from both the left and right must be the same (i.e., the left and right limits must "meet" at the point).

If all three conditions are met, then the function is continuous at that point.