End behaviour 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 words or arrow notation.
Example 2
Even degree, positive coefficient
Describe both ends of the graph using words or arrow notation.
Your turn
State the end behaviour using words or arrow notation.
Check answer
State the end behaviour using words or arrow notation.
Check answer
State the end behaviour using words or arrow notation.
Check answer
State the end behaviour using words or arrow notation.
Check answer
State the end behaviour using words or arrow notation.
Check answer
State the end behaviour using words or arrow notation.
State the end behaviour using words or arrow notation.
State the end behaviour using words or arrow notation.
State the end behaviour using words or arrow notation.
State the end behaviour using words or arrow notation.