Polynomial End Behavior
Polynomial end behavior is the direction the graph of a polynomial function goes as the input value goes "to infinity" on the left and right sides of the graph. There are four possibilities, as shown below.
Basic rules
With end behavior, the only term that matters with the polynomial is the one that has an exponent of largest degree. For example, if you have the polynomial only the matters in terms of end behavior.
This term will be of the form
A) When is positive and is an even number, the left and right sides of the graph both go to +infinity.
B) When is negative and is an even number, the left and right sides of the graph both go to -infinity.
C) When is positive and is an odd number, the left side goes to -infinity and the right side goes to +infinity.
D) When is negative and is an odd number, the left side goes to +infinity and the right side goes to -infinity.
What is the end behavior of
The largest exponent is 4, so the relevant term is is negative and is an even number so the end behavior matches that of B above.
What is the end behavior of the graph of the following polynomial function?