Factors determining a person's flexibility include age, genetics, and training habits. As individuals age, their muscles and joints tend to become stiffer, leading to decreased flexibility. Regular participation in activities like stretching, yoga, or dance can enhance flexibility by promoting muscle elasticity and joint health. Additionally, genetics can influence a person's natural range of motion and overall flexibility potential. Finally, warm-up routines prior to exercise play a crucial role in preparing muscles and tendons to improve flexibility and reduce injury risks.