Describe end behaviors of polynomial functions (LO 1.6.A)
Identify how leading coefficient sign affects end behavior
Distinguish even-degree vs odd-degree end behavior patterns
Use limit notation to express end behavior
End Behavior Rules
Even degree, a > 0:
\(\lim_{x\to-\infty}f(x)=+\infty,\;\lim_{x\to+\infty}f(x)=+\infty\)
Even degree, a < 0:
\(\lim_{x\to-\infty}f(x)=-\infty,\;\lim_{x\to+\infty}f(x)=-\infty\)
Odd degree, a > 0:
\(\lim_{x\to-\infty}f(x)=-\infty,\;\lim_{x\to+\infty}f(x)=+\infty\)
Odd degree, a < 0:
\(\lim_{x\to-\infty}f(x)=+\infty,\;\lim_{x\to+\infty}f(x)=-\infty\)
Why It Matters
End behavior tells you how a polynomial "escapes" toward infinity. It is determined solely by the leading term — the term with the highest degree. Understanding this is essential for sketching polynomial graphs and analyzing long-run trends in AP Precalculus.