Final answer:
To determine the end behavior of a function, examine the leading term and the degree of the function.
Step-by-step explanation:
To determine the end behavior of a function in mathematical analysis, you need to examine the leading term of the function. The leading term is the highest degree term in the function.
If the leading term has an even degree, the end behavior will be the same on both ends of the function. If the leading term has an odd degree, the end behavior will be different on each end of the function.
For example, if the leading term is x^2, the end behavior will be the same on both ends. If the leading term is x^3, the end behavior will be different on each end.