End Behavior of Polynomials

EVEN degree, NEGATIVE leading coefficient

down, down falls left, falls right x -> -∞, f(x) -> -∞ x -> ∞, f(x) -> ∞

ODD degree, POSITIVE leading coefficient

down, up falls left, rises right x -> -∞, f(x) -> -∞ x -> ∞, f(x) -> ∞

ODD degree, NEGATIVE leading coefficient

up, down rises left, falls right x -> -∞, f(x) -> -∞ x -> ∞, f(x) -> ∞

EVEN degree, POSITIVE leading coefficient

up, up rises left, rises right x -> -∞, f(x) -> -∞ x -> ∞, f(x) -> ∞