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Polynomial functions: degree and end behaviour

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Useful for: AP® Precalculus IB Math AA HL

Learn it The degree and the sign of the leading coefficient decide the end behaviour. Even degree: both ends go the same way (up if positive). Odd degree: ends go opposite ways (down-left, up-right if positive).

Example: Describe the end behaviour of y = −2x³ + 5x.

  1. Degree 3 (odd), leading coefficient −2 (negative).
  2. As x → −∞, y → +∞; as x → +∞, y → −∞: up on the left, down on the right.

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