13:
f is not symmetric, see
Limits at endpoints:
We see that f is continuous at 1 from the left but not from the right, so it is not continuous at 1. There is a jump discontinuity there.
Interpretation as asymptotes:
Horizontal asymptote
No horizontal asymptote at ∞, but a chance for oblique.
So no oblique there.
Now determine monotonicity using