Prove or disprove

Let f : R ---> R be a real function. Prove or disprove each of the following statements.

(a) If  f is continuous and range (f ) = R   then f is monotonic.

(b) If  f  is monotonic and range(f ) = R then f  is continuous.

            (c) If f  is monotonic and f  is continuous then range(f ) = R .