Polynomial Functions of Higher Degree

Polynomial Functions and their end-behavior:

When looking at the graphs of Any polynomial function of nth degree, there are two main things to note.
1) The number of x-intercepts= n
2) The number of Relative Extrema = n-1
Relative Extrema: Relative minimums and maximums

End Behavior:
When predicting the end behavior for a polynomial graph, you must look at the leading term/ highest power of x.

• If nth is even, both arrows will point in the same direction.
• If in is odd, the arrows will face in opposite directions.

Example:

Direction of End Behavior:

Right Hand End behavior: To find the direction of the right hand end behavior, you must look at the sign of the leading term.

Left hand end behavior: To find the direction of the left hand end behavior, you look at the exponent of the leading term to see if its arrow will point in the same direction as the right (even) or the opposite direction (odd). 

Example: Find the end behavior of both left and right sides of the polynomial function

The right hand end behavior: The arrow will point down on the right side because the sign on the leading term is negative (-3).

The left hand end behavior will also be pointing down because x is raised to an even power