If a vertex is removed from the graph $G$,
Lower Bound: number of components decreased by one = $k - 1$ (remove an isolated vertex which was a component)
Upper Bound: number of components = $n-1$ (consider a vertex connected to all other vertices in a component as in a star and all other vertices outside this component being isolated. Now, removing the considered vertex makes all other $n-1$ vertices isolated making $n-1$ components)
Therefore (C).