The video tutorial explains how to determine the end behavior of polynomial functions using the leading coefficient test. It covers the importance of knowing the degree and leading coefficient, and how these affect the graph's behavior. The tutorial also discusses the behavior of graphs with odd and even exponents, and positive or negative leading coefficients. It introduces formal notation to describe graph behavior and provides examples to illustrate these concepts.

What is the primary purpose of the leading coefficient test in determining end behavior?

• To determine the degree of the polynomial

• To identify the end behavior of the graph

• To calculate the y-intercept

• To find the roots of the polynomial

How does a graph with an odd degree and a positive leading coefficient behave?

• Falls to the right, falls to the left

• Falls to the right, rises to the left

• Rises to the right, falls to the left

• Rises to the right, rises to the left

What happens to the graph of a polynomial when the leading coefficient is negative?

• It shifts downwards

• It becomes a horizontal line

• It reflects about the x-axis

• It shifts upwards

In formal notation, what does it mean when x approaches infinity?

• The graph moves towards the origin

• The x-values decrease indefinitely

• The x-values increase indefinitely

• The graph becomes a vertical line

As x approaches negative infinity, what happens to the y-values in a graph with a positive leading coefficient and even degree?

• They approach negative infinity

• They remain constant

• They approach zero

• They approach positive infinity