Which two end behaviors are true of the follow

Question

Which two end behaviors are true of the following function?
h(t)=2t^4-t^3+6t^2+2t-8

1- As t →∞,h(t)→∞
2- As t →∞,h(t)→-∞
3- As t →-∞,h(t)→∞
4- As t →-∞,h(t)→-∞

 

 

answers to choose from
(a) 1 and 3 (b) 1 and 4

(c) 2 and 3 (d) 2 and 4

Answer 1

This is a 4th degree polynomial.  4 is an even number, which means that the left side and the right side of the curve go in the same direction (up or down).  Which direction it is depends on the coefficient of the highest order term, which is a fancy way to say the term that has the highest power of the variable (t).  In this case, the coefficient is positive, which means that the curve opens UP.  That means that as t approaches both -∞ and +∞, the value of the function approaches +∞.

 

So 1 is true and 3 is true, so the correct answer is (a)