The end behavior of a function is the direction toward which moves as extends to the left and the right infinitely. Analyzing each end individually, if extends upward, the behavior is expressed as
Alternatively, if extends downward, the behavior is
Consider the function
From the arrows on the graph, it can be seen that the left-end extends downward, while the right-end extends upward. Thus, the end behavior of can be expressed as follows.
A polynomial function with a term with the highest degree of where is the and is the of the the end behavior depends on and