Question

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

Answer 1

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.