Identify the point where continuity is being checked
Verify that the function is defined at that point
Compute the limit of the function as the input approaches that point
Check the left-hand limit and right-hand limit, if applicable
Confirm that both one-sided limits are equal
Confirm that the limit equals the function value at that point
If all three conditions hold, the function is continuous at that point
If any condition fails, the function is not continuous at that point