The video tutorial explains how to determine the end behavior of a polynomial function. It starts by identifying the degree and leading coefficient of the polynomial, then discusses how these factors influence the end behavior of the graph. The tutorial explains that for odd degrees, the graph can either fall left and rise right or rise left and fall right, depending on the sign of the leading coefficient. A positive leading coefficient results in the graph falling left and rising right. The video concludes with a formal representation of end behavior using infinity notation.

What is the degree of the polynomial 8 * X^11 - 2 * X^9 + 3 * X^6 + 4?

• 8

• 11

• 9

• 6

How does the degree of a polynomial affect its end behavior?

• It determines the number of turning points.

• It affects the symmetry of the graph.

• It indicates whether the graph will have a horizontal asymptote.

• It determines the direction of the graph's ends.

If a polynomial has an odd degree and a positive leading coefficient, what is the end behavior?

• Falls left, falls right

• Rises left, rises right

• Falls left, rises right

• Rises left, falls right

What happens to the graph of a polynomial as x approaches negative infinity if the leading coefficient is positive?

• The graph rises.

• The graph falls.

• The graph remains constant.

• The graph oscillates.

How can the end behavior of a polynomial be expressed using limits?

• By using derivatives

• By using integrals

• By using limits as x approaches infinity or negative infinity

• By using the quadratic formula