This segment demonstrates how to determine the time complexity of a function (n²logn + n) using Big O, Omega, and Theta notations. The speaker systematically compares the function to upper and lower bounds, illustrating the conditions for each notation and ultimately concluding that the function is θ(n²logn). This provides a clear understanding of how to apply these notations in practice. Big O, Omega, and Theta notations describe a function's growth rate relative to another. Big O (O) provides an upper bound, Omega (Ω) a lower bound, and Theta (Θ) a tight bound (both upper and lower). Factorial functions (e.g., n!) lack tight bounds; only upper and lower bounds can be determined. Choosing the tightest bound (Θ) is preferred when possible for accurate time complexity analysis. This segment focuses on the challenges of applying asymptotic notations to factorial functions. The speaker shows that for n!, finding a tight bound (θ) is impossible because the upper and lower bounds differ significantly. This highlights a crucial limitation of asymptotic analysis and demonstrates the use of Big O and Omega notations when a tight bound cannot be established.