Which is the ending behavior of the graph of the polynomial function f(x)=3x^6+30x^5+75x^4

A good way to find the end behaviors is to look at the number of the longest exponent in the equation. If it's even, then both ends go the same direction. If it's odd, then the ends go in two different directions. The highest exponent is even, so both ends go the same direction. Since the base of that highest exponent is a positive number, the effects aren't reversed, so the answer to this would be:
As x=-∞, y=∞; As x=∞, y=∞