Exploring End Behavior in Polynomial Functions

The video tutorial explains how to determine the end behavior of polynomial functions by examining the degree and leading coefficient. For even degree polynomials, both ends of the graph point in the same direction, determined by the sign of the leading coefficient. For odd degree polynomials, the ends point in opposite directions, also influenced by the leading coefficient. The tutorial provides examples to illustrate these concepts.

What two aspects of a polynomial function are essential to determine its end behavior?

• The leading coefficient and the constant term

• The number of terms and the degree

• The degree and the constant term

• The degree and the leading coefficient

How do you determine the degree of a polynomial function?

• By counting the number of terms

• By looking at the term with the smallest exponent

• By looking at the term with the largest exponent

• By adding the exponents of all terms

What happens to the end behavior of a polynomial function with an even degree?

• Both ends of the graph point in the same direction

• The graph oscillates

• One end points up and the other points down

• Both ends of the graph point in opposite directions

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

• One end points up and the other points down

• The graph oscillates

• Both ends point up

• Both ends point down

What determines whether the ends of an even-degree polynomial function point up or down?

• The smallest exponent

• The leading coefficient

• The number of terms

• The constant term

What is the end behavior of a polynomial function with an odd degree?

• Both ends point in the same direction

• Both ends point up

• Both ends point down

• The ends point in opposite directions

For an odd-degree polynomial function with a positive leading coefficient, what is the end behavior?

• Both ends point up

• The left end points down and the right end points up

• Both ends point down

• The left end points up and the right end points down

What happens to the end behavior of an odd-degree polynomial function if the leading coefficient is negative?

• The left end points up and the right end points down

• The left end points down and the right end points up

• Both ends point down

• Both ends point up

What is the primary factor to consider when determining the end behavior of a polynomial function?

• The leading coefficient

• The degree of the polynomial

• The constant term

• The number of terms

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

• The left end points up and the right end points down

• The left end points down and the right end points up

• Both ends point up

• Both ends point down