  We investigate the computational power of affine automata (AfAs) introduced
in [4]. In particular, we present a simpler proof for how to change the
cutpoint for any affine language and a method how to reduce error in bounded
error case. Moreover, we address to the question of [4] by showing that any
affine language can be recognized by an AfA with certain limitation on the
entries of affine states and transition matrices. Lastly, we present the first
languages shown to be not recognized by AfAs with bounded-error.
