Ultracold atoms with optical lattices provide a highly tunable system to measure the dynamic structure factor, S(q,ω), of an interacting one-dimensional (1D) Fermi gas. We use the two lowest hyperfine levels of the 6Li atom to form a pseudo-spin-1/2 system whose interactions are tunable via a Feshbach resonance. Bragg spectroscopy is used to measure the dynamic response of the 1D system to density (``charge'') mode excitations at a momentum q and frequency ω. In this thesis, we provide a quantitative comparison between the experimental result and the theoretical calculations based on Tomonaga-Luttinger theory.