The following information is about the function f.
•the domain of f is (−∞,−1)∪(−1,∞)
•f(0) = 0, f(1) =1/2
•f′(−1) is undefined, f′(0) = 0
•f′(x)>0 on (−∞,−1) and (0,∞). ,f′(x)<0 on="">0>
•f′′(−1) is undefined, f′′(1) = 0.
•f′′(x)>0 on (−∞,−1) and (−1,1), f′′(x)<0 on="">0>
•limx→−1f(x) =∞, limx→±∞f(x) = 1
(1) On what intervals is f concave up or down?
(2) Find all inflection points of f.
(3) Find the equation of the horizontal asymptote of f, or indicate that there is no horizontal asymptote.