Question 1042082
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F(x)=-x^3+3x^2

The leading term is -x^3 since this term has the largest exponent. So the end behavior of F(x) will be the same end behavior of y = -x^3


As x heads off to negative infinity, this means F(x) is heading off to positive infinity. This is another way of saying "as x decreases in value, y increases in value".



As x heads off to positive infinity, this means F(x) is heading off to negative infinity. This is another way of saying "as x increases in value, y decreases in value".



So to sum things up, the answer is 
<font color=red size=4>As x decreases in value, f(x) increases in value. As x increases in value, f(x) decreases in value.</font>


So the answer is <font color=red size=4>Choice B)</font>


Here's a graph to visually verify things.

{{{ graph( 500, 500, -10, 10, -10, 10, 0,-x^3+3x^2) }}}

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