One useful asymptotic notation is the upper bound, which is a function whose value, after an initial point, is always greater than the value of the function that you are studying. It is said that the upper bound grows faster than the function in question. A special notation, big-o (pronounced big oh) notation, is used to describe this growth. It is written f(x) is O(g(x)) and is read as f is big-oh of g. The formal mathematical definition is
Essentially, you are looking for a function whose behavior is as bad as or worse than the algorithm. You can then look at the result of very large inputs to this function and obtain an understanding of the bound of your algorithm.