We present new measurements of the inclusive forward-backward tt production asymmetry, AFB, and its dependence on several properties of the tt system. The measurements are performed with the full Tevatron data set recorded with the CDF II detector during pp collisions at √s=1.96  TeV, corresponding to an integrated luminosity of 9.4  fb−1. We measure the asymmetry using the rapidity difference Δy=yt−yt. Parton-level results are derived, yielding an inclusive asymmetry of 0.164±0.047(stat+syst). We establish an approximately linear dependence of AFB on the top-quark pair mass Mtt and the rapidity difference |Δy| at detector and parton levels. Assuming the standard model, the probabilities to observe the measured values or larger for the detector-level dependencies are 7.4×10−3 and 2.2×10−3 for Mtt and |Δy| respectively. Lastly, we study the dependence of the asymmetry on the transverse momentum of the tt system at the detector level. These results are consistent with previous lower-precision measurements and provide additional quantification of the functional dependencies of the asymmetry.