Answer:
down-up
Explanation:
Since 10x^9 - 4x is an odd function, we know its end behavior is either down-up or up-down.
(Picture a quadratic, which has a degree of 2. It's even, and its end behavior is up-up if it's positive or down-down if it's negative.)
10x^9 is positive, not negative, so we know its end behavior is down-up, not up-down.
(Picture x^3, which is a positive cubic. It's odd, and its end behavior is down-up. It would be up-down if it was -x^3.)