AP Calculus AB and BC glossary
End behavior
End behavior is what happens to a function's output as the input runs off to positive or negative infinity. It is stated as two limits at infinity, and for a rational function it is decided entirely by the highest-degree term on the top and the bottom.
Compare degrees. Bottom-heavy means the limit is zero. Equal degrees means the limit is the ratio of leading coefficients. Top-heavy means the function grows without bound, and if the gap is exactly one you get a slant asymptote.
The mistake
Assuming the two ends match. They often do not: an odd-degree polynomial runs to opposite infinities, and a function like arctan x flattens to different values on each side.
Appears in: Unit 1: Limits and Continuity