Exploring End Behavior of Polynomial Functions

The video tutorial explains how to determine the end behavior of polynomial functions in factored form. It covers methods using the degree and leading coefficient, as well as an alternative approach by examining the signs of each factor. The tutorial also demonstrates verifying end behavior through graphing, providing a comprehensive understanding of how polynomial functions behave as x approaches positive or negative infinity.

What does the end behavior of a polynomial function describe?

• The value of the function as x approaches zero

• The value of the function as x approaches positive or negative infinity

• The roots of the polynomial function

• The maximum and minimum points of the function

What is the first term in descending order when the polynomial is multiplied out?

• -x to the third

• x to the third

• -2x to the fifth

• 2x to the fifth

Tags

CCSS.HSA.APR.A.1

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

• Left end goes down, right end goes up

• Left end goes up, right end goes down

• Both ends go down

• Both ends go up

How can the end behavior of a polynomial function be determined using the signs of each factor?

• By adding the signs of each factor

• By multiplying the signs of each factor

• By subtracting the signs of each factor

• By dividing the signs of each factor

As x approaches positive infinity, what happens to the term -2 in the polynomial?

• It becomes positive

• It stays negative

• It becomes zero

• It becomes infinity

What is the end behavior of the polynomial as x approaches positive infinity?

• Negative infinity

• Undefined

• Positive infinity

• Zero

As x approaches negative infinity, what happens to the term x - 1?

• It approaches positive infinity

• It approaches negative infinity

• It becomes zero

• It stays constant

What is the end behavior of the polynomial as x approaches negative infinity?

• Positive infinity

• Negative infinity

• Zero

• Undefined

What is a method to verify the end behavior of a polynomial function?

• By calculating the derivative

• By graphing the function

• By solving for x

• By finding the roots

As x moves right on the graph, what happens to the function values?

• They approach positive infinity

• They approach negative infinity

• They stay constant

• They oscillate

Tags

CCSS.HSF-IF.C.7E