AP Precalculus / Unit 1: Polynomial and Rational Functions
1.6 Polynomial Functions and End Behavior
Notes
End behavior depends on the leading term $a_nx^n$:
- Even degree: both ends go the same direction (up if $a_n>0$).
- Odd degree: ends go opposite directions (right end up if $a_n>0$).
Practice
$p(x)=-2x^4+x$. As $x\to\infty$, $p(x)\to$
Even degree, negative leading coefficient.
$q(x)=3x^5-x^2$. As $x\to-\infty$, $q(x)\to$
Odd degree, positive leading coefficient: left end down.
End behavior of a polynomial is determined by:
For large $|x|$ the leading term dominates.
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