6: Limit at −∞:

No horizontal asymptote at −∞, but a chance for oblique.

In the second limit one can use l'Hospital's rule to show that x2^x goes to zero at minus infinity.
Oblique asymptote y = −x − 1 at −∞.

Limit at x = 0 from the left:

Vertical asymptote at x = 0.

Limit at x = 0 from the right:

Vertical asymptote at x = 0 confirmed.

Limit at ∞:

Horizontal asymptote y = 0 at ∞.

Answer