We report parameters that allow the dielectric functions <TEX>${\varepsilon}={\varepsilon}_1+i{\varepsilon}_2$</TEX> of <TEX>$AlAs_xSb_{1-x}$</TEX> alloys to be calculated analytically over the entire composition range <TEX>$0{\leq}x{\leq}1$</TEX> in the spectral energy range from 0.74 to 6.0 eV by using the dielectric function parametric model (DFPM). The <TEX>${\varepsilon}$</TEX> spectra were obtained previously by spectroscopic ellipsometry for x = 0, 0.119, 0.288, 0.681, 0.829, and 1. The <TEX>${\varepsilon}$</TEX> data are successfully reconstructed and parameterized by six polynomials in excellent agreement with the data. We can determine <TEX>${\varepsilon}$</TEX> as a continuous function of As composition and energy over the ranges given above, and <TEX>${\varepsilon}$</TEX> 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.