I'm working on my last Discrete Mathematics online question set at the moment, and I've finished everything except this one problem on Big O. Essentially, it gives me 5 functions, and I have to figure out if each one is O(x), Ω(x), or θ(x).
While I (at least vaguely) understand what each term means, I've not been able to get it correct, and I've only been allotted 3 attempts, so I wanted to get a solid answer before I press submit for the last time.
My understanding, graphically, is that if f(x) is always less than x after a certain point, then f(x) is O(x). If it's always more, than that would be Ω(x). If it's both above and below the function after the given point, though, then it's θ(x).
Here are the five functions I must check: f(x) = 10, g(x) = 3x + 7, h(x) = x^2 + x + 1, j(x) = 5log(x), and k(x) = floor(x).
As for my current answers, f(x) is both above and below x, so I said f(x) was θ(x). g(x) is both above and below, but since the question didn't specify I imagined it meant after x = 0, so I said g(x) was O(x). This is the same case for h(x). j(x) is always less than x, so I said j(x) was Ω(x), and k(x) was always less than or equal to as well, so I said it was Ω(x).
Thank you for your help.
Going through sections 9.2 and (parts of) 9.3 might improve your understanding of the concepts to answer questions of this kind in a much more comfortable manner.