  We construct families of irreducible representations for a class of quantum
groups $U_{q}(f_{m}(K,H)$. First, we realize these quantum groups as Hyperbolic
algebras. Such a realization yields natural families of irreducible weight
representations for $U_{q}(f_{m}(K,H))$. Second, we study the relationship
between $U_{q}(f_{m}(K,H))$ and $U_{q}(f_{m}(K))$. As a result, any finite
dimensional weight representation of $U_{q}(f_{m}(K,H))$ is proved to be
completely reducible. Finally, we study the Whittaker model for the center of
$U_{q}(f_{m}(K,H))$, and a classification of all irreducible Whittaker
representations of $U_{q}(f_{m}(K,H))$ is obtained.
