Graphical Behavior
Graphical Behavior
End Behavior
The end behavior of a rational function is what the graph looks like as x approaches positive and negative infinity. Unlike polynomial functions, the end behavior of rational functions has no pattern. Therefore, the asymptotes play a key role in determining a rational function’s end behavior.
Example 1 Determine the end behavior of the function.
As the x-values approach negative infinity, the graph approaches the horizontal asymptote from below. As the x-values approach positive infinity, the graph approaches the horizontal asymptote from above.