Sketch a possible graph for a function where f(-2) exists, lim as x->-2 exists, f is not continuous at x=-2, and lim x->1 doesn't exist.

Question

How do I make this graph exist at x->-2 but still be discontinuous?

Answer 1

just define f(-2) to be some value other than its limit.

f(x) = 2x for x ≠ -2
f(-2) = 0

The limit exists from both sides, but f is not continuous there.