As x approaches positive or negative infinity, if f(x) diverges, then it means that f(x) does not approach a set value. For example, in f(x) = x^2, as x approaches positive or negative infinity, f(x) does not approach a set value (it goes to positive infinity). On the other hand, if f(x) converges, then it means that f(x) does approach a set value. For example, in f(x) = e^x, as x approaches negative infinity, f(x) approaches 0; however, for the same function, as x approaches positive infinity, f(x) diverges.