13: D( f ) = ℝ; f is continuous on (−∞,1) ∪ (1,∞).
y-intercept: f (0) = 0; x-intercepts:

f = 0 gives x = 0.
f is not symmetric, see f = 0.
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 y = 0 at −∞.
No horizontal asymptote at ∞, but a chance for oblique.

So no oblique there.

Now determine monotonicity using f ′.

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Answer