Identify the function and the point where continuity is being tested
Check whether the function is defined at that point
Find the limit of the function as the input approaches that point
Evaluate the function at the point
Compare the left-hand limit and right-hand limit
Verify that the left-hand limit equals the right-hand limit
Verify that the limit equals the function value at the point
Conclude the function is continuous at the point if all three match
Repeat the same steps for every point in the interval if testing continuity on an interval