I'm at a complete loss for how to do this. Example for 1: The limit for f(x) is obviously 2, but is the limit for g(x) 2, or 3? It's different depending on which direction you come from. I've tried all combinations, as well as DNE (limit does not exist), but those are wrong. Is there something I'm missing here?

Step-by-step explanation:

As the graph of g(x) has a jump discontinuity at x = 1 the limit as x approaches 1 does not exist.

Therefore limit x---> 1 of f(x) + g(x) does not exist.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.