End Behaviors of Equations

The End Behavior of an equation is determined by two factors, the first being the highest exponent in the equation. the highest exponent determines how the ends act in terms of each other.

 where N is an odd number, the ends will act oppositely of each other

Ex.  Graph:



 where N is an even number, the ends will act the same as each other

Ex.  Graph

The Second Factor in the finding the end behaviors is whether or not the leading coefficient is positive or if it is negative. this determines whether as X approaches infinty if Y will also approach infinty, or if it will approach negative infinty, and whether or not as -X approaches infinty if Y will do the same or approach positive infinty. This can be summed up graphically in the following way:

If leading coefficient of  is negative and N is even
 

If the leading coefficient of is positive, and N is even



The same goes for odd functions, so if the leading coefficient of  is negative and N is Odd

 

 

If the leading coefficient of  is positive, and N is odd