18: D( f ) = ℝ; f is continuous there.
y-intercept: f (0) = −1; x-intercepts: f = 0 not possible to solve.
f is not symmetric since f (−x) is not equal to f (x) nor to -f (x) (try e.g. x = π).
Limits at endpoints:

The first limit can be deduced using the estimate x − cos(x) ≤ x + 1, the second limit using x − cos(x) ≥ x − 1,
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