Question 940762
g(x) is the exponential function (in this case g(x) = 2^x), but 2. is more correct.


2. If we interpret "eventually exceed" as "x increases to +infinity", then this statement is always true for increasing exponential functions. For example, if f(x) = 100000x^2 and g(x) = 1.0001^x, then g(x) will eventually overtake f(x). In asymptotic notation, we write *[tex \large f(x) = o(g(x))], i.e. f(x) is asymptotically smaller than g(x).


4. is true for this quadratic, but not true in general.