5: D( f ) = ℝ; f is continuous there.
y-intercept: f (0) = 1; x-intercepts: f = 0 not possible.
f (−x) = f (x), hence f is even.
Limits at endpoints:

Interpretation as asymptotes:
Horizontal asymptote y = 0 at −∞.
Horizontal asymptote y = 0 at ∞.

Now determine monotonicity using f ′.

Next hint
Answer