56. If k is a real number and f(x) = sin(1/x) for x not equal to 0, and f(x)=k for x=0

and if the graph of f is not a connected subset of the plane, then the value of k

(A) could be -1

(B) must be 0

(C) must be 1

(D) could be less than 1 and greater than -1

(E) must be less than -1 or greater than 1

Answer is (E)

Can anyone help on this? I can make sense of (E), but how do you prove it?