Determining End Behavior of Graphs by Analyzing Equations

This video tutorial explains how to determine the end behavior of graphs by analyzing their equations. It covers power functions, focusing on even and odd exponents, and discusses how these affect graph shapes. The tutorial also explains how to identify increasing and decreasing functions on specific intervals. A significant portion is dedicated to understanding the end behavior of polynomials, emphasizing the importance of the lead term. The video concludes with practical examples of analyzing polynomial end behavior.

What is a power function and how is it represented mathematically?

What does it mean for a function to increase or decrease on a specific interval?

What are the four situations that can occur regarding the lead term of a polynomial?

Describe the end behavior of a polynomial function with an even degree and a positive lead coefficient.

How does the end behavior differ between polynomials with odd and even degrees?

Explain how to determine the end behavior of a polynomial function.

Discuss the common misunderstandings students have regarding the end behavior of functions.