Use the given graph to determine the limit, if it exists.

find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x.

my choices are:

1; 1
-1; 4
4; -1
does not exist; does not exist

Well, check the graph.

notice the "holes" on each line, it means that point is not part of the line, notice the dot down below at (2,1), meaning when x = 2, f(x) = 1.

now, a limit, is something the "x" is approaching to, it may never get there, but for a limit that doesn't matter, what matters is that, the value is approaching is ever consistent, though it may never get there.

as "x" comes from the left, notice, f(x) is, 4 and then 4 and 4 again and again 4 and again 4, so the one-sided-limit from the left is 4, even though at x = 2 it drops down.

as "x" comes from the right, f(x) is, -1, and then -1, and -1 and -1 again, and -1 again, so the one-sided-limit from the right is -1.