Yeah I understand. I was describing how I did it in Algebra II. They would give up f(n) = 5x^3 +4x + 8 and we would know that it was O(x^3).
We also understood that it was as n -> infinity, hence why f(n) = 2x^4 would have a larger growth rate than g(n) = x^2 + 5000. When you're talking about scalability when programming, you're going to have to understand big-O, how constant factors come into play (why Floyd-Warshall at O(n^3) is often better in practice), and how big-\Theta works. If not, you're eventually going to make a mistake and slow everything down.
We also understood that it was as n -> infinity, hence why f(n) = 2x^4 would have a larger growth rate than g(n) = x^2 + 5000. When you're talking about scalability when programming, you're going to have to understand big-O, how constant factors come into play (why Floyd-Warshall at O(n^3) is often better in practice), and how big-\Theta works. If not, you're eventually going to make a mistake and slow everything down.