May I ask how many solved examples of similar problems you have read and understood?
How do you determine the best "big-Oh" form?
Use the results of Table 1 to determine the best “big-Oh” form for the following function f: Z^+→ R.
f(n) = 3n + 7
Table 1 (I'm not sure how to write tables so I used the dash (-----):
Big-Oh Form ------------------------ Name
O(1) --------------------------------- Constant
O(log_2 n) -------------------------- Logarithmic
O(n) --------------------------------- Linear
O(n log_2 n) ------------------------ n log_2 n
O(n^2) ------------------------------ Quadratic
O(n^3) ------------------------------ Cubic
O(n^m), m = 0, 1, 2, 3,... ------- Polynomial
O(c^n), c > 1 ----------------------- Exponential
O(n!) -------------------------------- Factorial