Understanding End Behavior of Polynomial Functions

The video tutorial explains how to determine the end behavior of polynomial functions based on the degree and the sign of the leading coefficient. It covers four cases: even degree with positive or negative leading coefficients, and odd degree with positive or negative leading coefficients. Each case is illustrated with examples, and the importance of graphing the function for verification is emphasized.

What two factors are essential to determine the end behavior of a polynomial function?

• The degree and the leading coefficient

• The number of terms and the degree

• The degree and the constant term

• The leading coefficient and the constant term

For a polynomial with an even degree and a positive leading coefficient, what happens to the function as x approaches positive infinity?

• The function oscillates

• The function approaches positive infinity

• The function approaches zero

• The function approaches negative infinity

If a polynomial has an even degree and a positive leading coefficient, what is the end behavior as x approaches negative infinity?

• The function approaches negative infinity

• The function approaches zero

• The function oscillates

• The function approaches positive infinity

What is the end behavior of a polynomial with an even degree and a negative leading coefficient as x approaches positive infinity?

• The function approaches negative infinity

• The function approaches zero

• The function approaches positive infinity

• The function oscillates

For a polynomial with an even degree and a negative leading coefficient, what happens as x approaches negative infinity?

• The function oscillates

• The function approaches negative infinity

• The function approaches zero

• The function approaches positive infinity

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient as x approaches positive infinity?

• The function approaches negative infinity

• The function oscillates

• The function approaches zero

• The function approaches positive infinity

For a polynomial with an odd degree and a positive leading coefficient, what is the behavior as x approaches negative infinity?

• The function approaches positive infinity

• The function oscillates

• The function approaches zero

• The function approaches negative infinity

What happens to a polynomial with an odd degree and a negative leading coefficient as x approaches positive infinity?

• The function oscillates

• The function approaches negative infinity

• The function approaches zero

• The function approaches positive infinity

For a polynomial with an odd degree and a negative leading coefficient, what is the end behavior as x approaches negative infinity?

• The function approaches positive infinity

• The function approaches zero

• The function approaches negative infinity

• The function oscillates

What is a recommended method to verify the end behavior of a polynomial if unsure?

• Find the roots

• Calculate the derivative

• Graph the function

• Evaluate the constant term