Determine the end behavior of a polynomial

The video tutorial explains how to determine the end behavior of a polynomial function using the leading coefficient test. It emphasizes the importance of the degree and leading coefficient in predicting whether the graph of the function will rise or fall as it approaches infinity. The tutorial also covers how to express end behavior in terms of x approaching positive or negative infinity, providing a clear understanding of how these concepts apply to graphing polynomial functions.

What is the significance of the leading coefficient in determining the end behavior of a polynomial function?

Describe the end behavior of the function as x approaches positive and negative infinity.