This segment demonstrates a practical method for comparing the growth of two functions (n² and n³) by sampling values and observing the trends. The speaker effectively illustrates how a small number of test cases can provide sufficient evidence to determine which function dominates. This approach is valuable for its simplicity and intuitive understanding. This segment showcases a more advanced technique for comparing the growth of complex functions (n²log n and (n log n)^10) using logarithms. The speaker meticulously applies logarithmic properties to simplify the expressions and determine which function grows faster. This method is particularly useful when dealing with functions that are difficult to compare directly. Comparing functions involves determining upper and lower bounds. Methods include: 1) Sampling values to observe growth; 2) Applying logarithms to simplify and compare. Logarithmic properties (e.g., log(ab) = log a + log b) are crucial for this method. Examples show comparing n², n³, and more complex functions using these techniques. Asymptotic behavior (e.g., n² and 3n² are asymptotically equal) is also considered.