First-principle calculations with quasiparticle corrections are performed on the optical and electronic properties of functionalized armchair graphene nanoribbons (AGNRs). W8, W9 and W10 AGNRs are chosen based on the width (W) index, n. The functional groups (X = CH₃, NH₂, NO₂ and OH) are selected for the functionalized AGNRs (W(n)-X). Most of the functional groups enlarge the GW band gaps of W8 and W9, and reduce the GW band gap of W10. The variation of band gaps is analyzed in terms of the bonding characteristics. In all of the W10-X structures, most of the exciton wavefunctions are located on the bigger segments divided by the functional groups. Additionally, W10-NO₂ is a potential candidate for luminescence and photovoltaic devices due to its strong optical absorption and small exciton binding energy.