Our previous computational studies of two-dimensional quantum waveguide structures formed at the interface of the A1GaAs/GaAs heterostructure have focused on systems with centered attractive potential wells. From those studies we direct our attention to the quantum waveguide structures with an attractive potential well placed asymmetrically in the transverse direction. In particular, we are interested in the conductance spectrum for higher energy regimes where Fano resonances are the dominant resonance form. Of interest is the change and progression of Fano resonance peaks as a function of both the potentials' depth and offset, especially as it relates to the Breit-Wigner resonance forms observed in lower energy regimes. To accomplish this, the hard-wall models and Fortran code in our previous work have been expanded to include the asymmetrical positioning through solving the single-electron Schrodinger and associated equations used in the tight-binding Hamiltonian and recursive Green's functions. The observed Fano resonance structures are fitted to their characteristic equations through the use of zero-pole pairs.