The degree of a polynomial function affects the shape of its graph and determines the maximum number of turning points, or places where the graph changes direction. It also affects the end behavior, or the directions of the graph to the far left and to the far right.
For polynomial functions of degree one or greater, there are four types of end behavior as you move to the left and move to the right, away from the origin: up and up, down and down, down and up, and up and down.
| Up and Up | Down and Down | Down and Up | Up and Down |
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You can determine the end behavior of a polynomial function of degree n from the leading term
| n Even | n Odd | |
|---|---|---|
| a Positive | Up and Up | Down and Up |
| a Negative | Down and Down | Up and Down |
Problem 2 Describing End Behavior of Polynomial Functions
Consider the leading term of each polynomial function. What is the end behavior of the graph? Check your answer with a graphing calculator.
Think
What do a and n represent?
a is the coefficient of the leading term. n is the exponent of the leading term.
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The leading term is
Check
The solution checks.
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The leading term is
Check
The solution checks.
✓ Got It?
- Consider the leading term of
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions