Question

Wondering how to figure out limits from a piece-wise function without having to graph it, as to save time on exams

Answer 1

If the limit point is at a discontinuity of the function, the direction of the limit tells you which function to use in your limit. There's no particular need to graph it if you're not asked to.

Answer 2

So is that where the statements after the "if" are useful?

Answer 3

Yes. So for example, part (a) wants to know the limit as x->0 from the left. If you're to the left of zero, of course you should use the top function (x+2), so the limit is equal to 2.