Exploring 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 constant term

• The degree and the leading coefficient

• The leading coefficient and the constant term

• The number of terms and the degree

If a polynomial function has an even degree and a positive leading coefficient, what happens to f(x) as x approaches positive infinity?

• f(x) approaches negative infinity

• f(x) approaches zero

• f(x) approaches positive infinity

• f(x) oscillates

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

• f(x) approaches negative infinity

• f(x) approaches positive infinity

• f(x) oscillates

• f(x) approaches zero

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

• f(x) approaches positive infinity

• f(x) approaches zero

• f(x) oscillates

• f(x) approaches negative infinity

For a polynomial function with an even degree and a negative leading coefficient, what happens to f(x) as x approaches negative infinity?

• f(x) approaches negative infinity

• f(x) approaches zero

• f(x) approaches positive infinity

• f(x) oscillates

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

• f(x) approaches negative infinity

• f(x) approaches zero

• f(x) approaches positive infinity

• f(x) oscillates

For a polynomial function with an odd degree and a positive leading coefficient, what happens to f(x) as x approaches negative infinity?

• f(x) oscillates

• f(x) approaches positive infinity

• f(x) approaches zero

• f(x) approaches negative infinity

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

• f(x) approaches positive infinity

• f(x) approaches zero

• f(x) oscillates

• f(x) approaches negative infinity

For a polynomial function with an odd degree and a negative leading coefficient, what happens to f(x) as x approaches negative infinity?

• f(x) approaches negative infinity

• f(x) oscillates

• f(x) approaches zero

• f(x) approaches positive infinity

What is the best approach if you are unsure about the end behavior of a polynomial function?

• Consider the highest degree term only

• Look at the number of terms

• Graph the function and analyze the graph

• Check the constant term