Identify the function and the point where continuity is being tested
Check whether the function is defined at that point
Compute the limit of the function as the input approaches that point
Compute the function value at that point
Compare the limit and the function value
Verify that the limit exists
Verify that the left-hand limit and right-hand limit are equal
Conclude the function is continuous if the limit exists and equals the function value
Conclude the function is not continuous if any condition fails