Question 1153150
end behavior of a graph is determined by the value of x when x approaches 
positive infinity and when x approaches negative infinity.


it turns out that the leading coefficient and whether the exponent is odd or even determines the end behavior.


as the value of x in either direction is controlled by the term that has the highest value exponent, that term controls the end behavior.


here's a reference.


<a href = "https://www.varsitytutors.com/hotmath/hotmath_help/topics/leading-coefficient-test" target = "_blank">https://www.varsitytutors.com/hotmath/hotmath_help/topics/leading-coefficient-test</a>


<a href = "https://www.varsitytutors.com/hotmath/hotmath_help/topics/end-behavior-of-a-function" target = "_blank">https://www.varsitytutors.com/hotmath/hotmath_help/topics/end-behavior-of-a-function</a>