For question #1:

(c) is wrong (f(2) = ? f(-1) = ?)

Answer (c) before answering (a).

Answer (b) before answering (d).

he surjectivity of functions from to is asking if it ever goes to minus-infinity, and if it ever goes to infinity. That's including when x goes to plus or minus infinity. Basically, you're asking if it's bounded above, and if it's bounded below.

Of course, there's a little bit more involved. For instance, the function y = 1/x is continuous everywhere except x=0, and is neither bounded above nor bounded below, but isn't surjective onto because it never takes the value 0.

Technically, you'll use the Intermediate Value Theorem and an analysis of the function's continuity to derive that it's surjective (if it is surjective).

For question 2, it's simple enough to directly check if f is injective, and chekc if f is surjective. However, if you know linear algebra, a useful observation is that L(x1, x2) = f(x1, x2) - (3, 0) defines a linear map L. So it's a simple argument to see that whether f is injective (or surjective) will be the same as whether L is injective (or surjective) - and with linear maps, there are some tools you can use to answer that question.