Question

sketch the graph of a function f that satisfies the given conditions: The domain of f is all x except x=1.
x=1 is a vertical asymptote
lim f(x)=1
x->(infinity)
f(2)=0, f(0)=0, f(-1)=-1
f'(x)>0 on (1,infinity)U(-1,0)
f'(x)<0 on (0,1)U(-infinity,-1)
f"(x)<0 on (1,infinity)U((-1/2),1)
f"(x)>0 on (-infinity, (-1/2))

Answer 1

This is the first part, do you have something on limit as x->-inf ?