Determining End Behavior of Polynomials

This lesson explains how to determine the end behavior of polynomials by comparing them to power functions. It covers the characteristics of power functions, the impact of even and odd powers on end behavior, and the effect of negative coefficients. The lesson also discusses how to determine the degree of a polynomial and provides examples to illustrate these concepts. The key takeaway is understanding how the highest degree term influences the polynomial's behavior as X approaches infinity or negative infinity.

What is a power function?

• A function with multiple terms and positive integer powers

• A function with a single term and a positive integer power

• A function with multiple terms and any real number power

• A function with a single term and any real number power

What happens to the end behavior of an even power function as x approaches infinity?

• Both sides go towards negative infinity

• Right side goes up, left side goes down

• Both sides go towards positive infinity

• Right side goes down, left side goes up

How does the end behavior of an odd power function differ from an even power function?

• Both sides go towards positive infinity

• Right side goes down, left side goes up

• Right side goes up, left side goes down

• Both sides go towards negative infinity

What effect does multiplying by a negative number have on the graph of a polynomial?

• It shifts the graph upwards

• It shifts the graph downwards

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

How can you determine the degree of a polynomial?

• By adding the powers of all terms

• By counting the number of terms

• By finding the term with the highest power

• By looking at the first term in any form

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

• Right side goes down, left side goes up

• Right side goes up, left side goes down

• Both sides go towards negative infinity

• Both sides go towards positive infinity

What happens to the polynomial's behavior as x becomes very large?

• The polynomial behaves like a constant

• The highest degree term dominates

• The lowest degree term dominates

• The polynomial behaves unpredictably