Mathematics · Polynomial Functions · Topic 12 · 12 of 18
End Behavior and Turning Points
Use degree, leading coefficient, and degree bounds to describe a graph.
Leading Coefficient TestDegree parity and coefficient sign determine both ends.
Turning-point boundA degree n polynomial has at most n−1 turning points.
ContinuityPolynomial graphs are smooth and unbroken.
Example
Degree 5 with negative leading coefficient
The left end rises, the right end falls, and the graph has at most four turning points.