Graphical Behavior

Example 3

Determine the end behavior of the function.

Because there is no horizontal asymptote, the end behavior is determined by finding the ratio of the leading terms: or y = -x. Therefore, g(x) has the same end behavior as the linear function . As the x-values approach negative infinity, the y-values approach positive infinity. As the x-values approach positive infinity, the y-values approach negative infinity.