8: D( f ) = ℝ; f is continuous there.
y-intercept: f (0) = 0; x-intercepts: f = 0 yields x = 0, x = −5/2.
f is not symmetric, see f = 0.
Limits at endpoints:

Interpretation as asymptotes:
No horizontal asymptote at −∞, but a chance for oblique.

So no oblique there.
No horizontal asymptote at ∞, but a chance for oblique.

So no oblique there.

Now determine monotonicity using f ′.

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Answer