Answer: Choice D
y goes to negative infinity for both cases of x going to infinity or negative infinity.
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Step-by-step explanation:
The degree of this function is 4, as it is the largest exponent. The even number degree tells us that the end behavior is that either
case A: the endpoints rise together
or
case B: the endpoints fall together
In short, the endpoints are more or less mirror copies going in the same direction.
In this case, both endpoints fall together as the leading coefficient (-3) is negative. As x heads off to infinity, y will go to negative infinity. As x heads off to negative infinity, y will also go to negative infinity. Regardless of which direction x goes, y will go downhill.
note: your book may refer to this as "fall to the left and fall to the right".