Which best describes the end behavior of y=-2x^3? as x > 0 increases, f(x) increases. as x < 0 decreases, f(x) increases. as x > 0 increases, f(x) decreases. as x < 0 decreases, f(x) decreases. as x > 0 increases, f(x) increases. as x < 0 decreases, f(x) decreases. as x > 0 increases, f(x) decreases. as x < 0 decreases, f(x) increases.

Choice D

As x increases, f(x) decreases; As x decreases, f(x) increases

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This is an odd function (not odd as in strange, but odd as in not even). So the end behavior of this function has the left side going to positive infinity and the right side going to negative infinity.

Informally, it rises to the left and falls to the right. Check out the attached image for the graph.

More formally, as x gets larger, then y = f(x) gets smaller. In reverse, if x gets smaller or more negative, then y = f(x) gets larger. The negative out front of y = -2x^3 is the reason why x and y go in opposite directions for the end behavior (one gets larger while the other gets smaller).

step-by-step explanation: