A function is even if f(-x) = f(x) and odd if f(-x) = -f(x). In your case

Is this even, odd, or neither?

You get a horizontal asymptote when . If this case your limits are either positive or negative infinity. So you have no horizontal asymptotes.

-Dan

Edit: You do have a "slant" asymptote if you need to look for one of those. The slant asymptote is y = x + 1.