End Behavior of Polynomials

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End Behavior

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ODD degree, NEGATIVE leading coefficient

up, down

rises left, falls right

x -> -∞, f(x) -> -∞

x -> ∞, f(x) -> ∞

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

3

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ODD degree, POSITIVE leading coefficient

down, up

falls left, rises right

x -> -∞, f(x) -> -∞

x -> ∞, f(x) -> ∞

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

4

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EVEN degree, NEGATIVE leading coefficient

down, down

falls left, falls right

x -> -∞, f(x) -> -∞

x -> ∞, f(x) -> ∞

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

5

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EVEN degree, POSITIVE leading coefficient

up, up

rises left, rises right

x -> -∞, f(x) -> -∞

x -> ∞, f(x) -> ∞

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