End behavior
SAT glossary · Math
Definition
What a polynomial does as x →± ∞, fixed entirely by the leading term: even degree sends both ends the same way, odd degree sends them opposite ways, and a negative leading coefficient flips the picture.
End behavior in plain English
End behavior describes what a polynomial's graph does way out at the far left and far right edges — does it shoot up toward positive infinity, or plunge down toward negative infinity? The good news is you don't need to graph anything to figure this out: it's completely controlled by just the highest-power term. If the degree (highest exponent) is even, both ends of the graph point the SAME direction; if the degree is odd, the two ends point OPPOSITE directions from each other. Then the sign of the leading coefficient (the number in front of that highest term) decides which way: positive keeps the 'default' direction, negative flips the whole picture upside down.
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