# Seatwork (Asymptotic Analysis 1)

Given the following pair of functions, choose all asymptotic relationships that apply ($O(g(n)), \Omega(g(n)), \Theta(g(n))$).

1. $f(n) = n^2 + 2$, $g(n) = 2n^3$
2. $f(n) = 10n + 2$, $g(n) = n^2 + 1$
3. $f(n) = 5\log_2 n + 2$, $g(n) = n+3$
4. $f(n) = n\log_2 n + 2$, $g(n) = 2n^2+n$
5. $f(n) = 2^n$, $g(n) = 5n^5$
6. $f(n) = \log_2 n$, $g(n) = \sqrt{n +2}$
7. $f(n) = \frac{\sqrt{n +2}}{(\log_2 n)}$, $g(n) = \log_4 {(\log_2 n)}$