End
Behavior
The appearance of a graph as
it is followed farther and farther in either direction. For polynomials,
the end behavior is indicated by drawing the positions of the arms
of the graph,
which may be pointed up or down. Other graphs may
also have end behavior indicated in terms of the arms, or in
terms of asymptotes or limits.
Polynomial End Behavior:
1. If the degree n of a polynomial is even, then the arms of the graph
are either both up or both down.
2. If the degree n is odd, then one arm of the graph is up and one is
down.
3. If the leading coefficient a_{n} is
positive, the right arm of the graph is up.
4. If the leading coefficient a_{n} is
negative, the right arm of the graph is down.
See
also
Polynomial facts
