We report parameters that allow the dielectric functions ${varepsilon}={varepsilon}_1+i{varepsilon}_2$ of $AlAs_xSb_{1-x}$ alloys to be calculated analytically over the entire composition range $0{leq}x{leq}1$ in the spectral energy range from 0.74 to 6.0 eV by using the dielectric function parametric model (DFPM). The ${varepsilon}$ spectra were obtained previously by spectroscopic ellipsometry for x = 0, 0.119, 0.288, 0.681, 0.829, and 1. The ${varepsilon}$ data are successfully reconstructed and parameterized by six polynomials in excellent agreement with the data. We can determine ${varepsilon}$ as a continuous function of As composition and energy over the ranges given above, and ${varepsilon}$ can be converted to complex refractive indices using a simple relationship. We expect these results to be useful for the design of optoelectronic devices and also for in situ monitoring of AlAsSb film growth.