Hi, I am really stuck on both parts of this analysis question could somebody please help me? I don't really know how to start, I have the definition for part a but nothing else.

1.(a). For a function (f) from the reals to the reals define what is meant by f(x) tends to infinity as x tends to negative infinity and prove it holds if and only if whenever a real sequence (x_n) tends to negative infinity f(x_n) tends to infinity.

b). If a function f from the reals to the reals is continuous and tends to infinity as x tends to negative infinity show that there exists a sequence x_n which tends to negative infinity as x tends to infinity such that f(x_n)=n for all but a finite number of n.