Group the following functions into classes so that two functions f(n) and g(n) are in the same class if and only if f(n) belongs to theta(g(n). List the classes in increasing order of magnitude of its members. A class may consist of one or more members. f_1 (n) = 6000 f_2(n) = (lg n)^6 f_3(n) = 3^n f_4(n) = lg n f_5(n) = n + lg n f_6(n) = n^3 f_7(n) = n^2 lg n f_8(n) = n^2 - 100n f_9(n) = 4n + squareroot n f_10(n) = lglg n^2 f_11(n) = n^0.3 f_12(n) = n^2 f_13(n) = lg n^2 f_14(n) = squareroot n^2 + 4 f_15(n) = 2^n