Graphical Behavior
End Behavior
Example 2
Describe the end behavior of f(x) = 3x7 + 5x + 1004.
Step 1. Consider the degree.
The exponent says that this is a 7th degree polynomial, so the graph will behave roughly like a cubic: the ends will point in opposite directions.
Step 2. Consider the leading coefficient.
Since the sign on the leading coefficient is positive, the graph will be increasing from lower left to upper right.