End behavior of a polynomial
Use the leading term to predict what happens at both ends of the graph.
- Find the degree and the sign of the leading coefficient.
- An even degree gives the same direction at both ends; an odd degree gives opposite directions.
- A positive leading coefficient makes the right end rise; a negative one makes it fall.
| Degree | Leading coefficient | Left end | Right end |
|---|---|---|---|
| Even | Positive | Rises | Rises |
| Even | Negative | Falls | Falls |
| Odd | Positive | Falls | Rises |
| Odd | Negative | Rises | Falls |
Example 1
Odd degree, negative coefficient
Describe both ends of the graph using limit notation.
Left end rises; right end falls.
Example 2
Even degree, positive coefficient
Describe both ends of the graph using limit notation.
Left end rises; right end rises.
Your turn
5 practice questions0 of 5 answers checked
Question 1
State the end behavior using limit notation.
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Question 2
State the end behavior using limit notation.
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Question 3
State the end behavior using limit notation.
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Question 4
State the end behavior using limit notation.
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Question 5
State the end behavior using limit notation.
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State the end behavior using limit notation.
State the end behavior using limit notation.
State the end behavior using limit notation.
State the end behavior using limit notation.
State the end behavior using limit notation.