Answer: A) both ends go up
As x gets larger in the positive direction, then so does y = f(x). If x heads off in the negative direction, then y = f(x) still increases. So we can say that the function rises to the left and rises to the right; or in short "both ends go up". If you expanded the polynomial out, then the leading term would be 1x^6. The degree 6 (largest exponent) tells us that the endpoints either go up together or down together. In this case they both go up together because of the positive leading coefficient of 1.
This can be seen with a graph as shown below. The graph looks like a parabola, but it's actually not. The reason why there's a similarity is due to the fact that (x+2)^6 = [ (x+2)^3 ] ^2. Put another way, I'm using an idea similar to x^6 = (x^3)^2. So anything to the 6th power has similar traits to quadratics.