Polynomial Degree and End Behavior

The video tutorial explains how to determine the end behavior of polynomials by focusing on the degree and leading coefficient. It emphasizes the importance of arranging polynomials in descending order of power and understanding whether the degree is odd or even, and if the leading coefficient is positive or negative. The tutorial uses graph representations to illustrate how these factors influence the end behavior, showing how the graph behaves as x approaches positive or negative infinity. The concept of left and right hand behavior is also discussed, helping students visualize the graph's direction.

What is the first step in determining the end behavior of a polynomial?

• Calculate the derivative of the polynomial

• Arrange the polynomial in descending order of power

• Identify the roots of the polynomial

• Find the constant term

What is the leading coefficient of a polynomial?

• The sum of all coefficients

• The coefficient of the term with the highest power

• The constant term of the polynomial

• The coefficient of the term with the lowest power

How can you determine if a polynomial's degree is even or odd?

• By counting the number of terms in the polynomial

• By finding the sum of all coefficients

• By looking at the highest power of the polynomial

• By checking if the polynomial has a constant term

What does a graph with an odd degree and a positive leading coefficient generally look like?

• It rises to the left and falls to the right

• It is a vertical line

• It falls to the left and rises to the right

• It is a horizontal line

What does the end behavior of a polynomial tell us?

• The roots of the polynomial

• The y-intercept of the graph

• The behavior of the graph as x approaches infinity

• The exact shape of the graph

As x approaches negative infinity, what happens to the graph of a polynomial with an odd degree and positive leading coefficient?

• The graph rises

• The graph falls

• The graph remains constant

• The graph oscillates

As x approaches positive infinity, what happens to the graph of a polynomial with an odd degree and positive leading coefficient?

• The graph oscillates

• The graph falls

• The graph remains constant

• The graph rises

What is the left-hand behavior of a polynomial?

• The behavior at the x-intercept

• The behavior at the y-intercept

• The behavior as x approaches negative infinity

• The behavior as x approaches positive infinity

What is the right-hand behavior of a polynomial?

• The behavior as x approaches negative infinity

• The behavior as x approaches positive infinity

• The behavior at the y-intercept

• The behavior at the x-intercept

Why is it important to understand the end behavior of a polynomial?

• To calculate the derivative of the polynomial

• To find the roots of the polynomial

• To predict the behavior of the graph at extreme values of x

• To determine the exact shape of the graph