While changes in resonant Raman scattering measurements are commonly used to measure the effect of chemical functionalization on single-walled carbon nanotubes, the precise effects of functionalization on these spectra have yet to be clearly identified. In this density functional theory study, we explore the effects of functionalization on both the nanotube resonance energy and frequency shifts in radial breathing mode. Charge transfer effects cause a shift in the first Van Hove singularity spacings, and hence resonance excitation energy, and lead to a decrease in the radial breathing mode frequency, notably when the Fermi level decreases. By varying stochastically the effective mass of carbon atoms in the tube, we simulate the mass effect of functionalization on breathing mode frequency. Finally, full density functional calculations are performed for different nanotubes with varying functional group distribution and concentration using fluorination and hydrogenation, allowing us to determine overall effect on radial breathing mode and charge transfer. The results concur well with experiment, and we discuss the importance when using Raman spectroscopy to interpret experimental functionalization treatments