I've been struggling with this problem for, I kid you not, a week off and on. I get part of it sketched but then I think I've contradicted myself and I start second guessing. I suppose I'll write what I think it says and correct me based on that.

$\displaystyle \lim \limits_{x \to -\infty} f(x)=2$

I take this to mean that as x approaches y=2, we drop down to negative infinity. I've drawn a horizontal asymptote here but I'm unsure if that's correct.

$\displaystyle \lim \limits_{x \to -1^-} f(x)=\infty$

As we get to negative 1 from the left, go north. This means we never actually hit -1 from the right, we just approach it infinitly right?

$\displaystyle \lim \limits_{x \to -1^+} f(x)=5$

Does this mean from the other side we start drawing a line at point (-1,5) and go where? This is where after we go right a bit... This must join up to something else.

fis continuous from the right at -1

Does this information pairs up with the limit just above this one?

$\displaystyle \lim \limits_{x \to 2^-} f(x)=-\infty$

At this point I'm lost. I think I've messed something up before here and by the time I get to this point it's game over.

$\displaystyle \lim \limits_{x \to 2^+} f(x)=+\infty$

Second last piece of information.

$\displaystyle \lim \limits_{x \to \infty} f(x)=-2$

Just draw an asymptote here right?

If time permits please show me how to appraoch this type of question. What should I look for first? What should I tackle last? I double checked all the equations, hopefully there are no typos.