Question 1042082: Please help me solve this problem:
Which of the following describes the end behavior of the equation below?
F(x)=-x^3+3x^2
a) As x decreases in value, f(x) decreases in value. As x increases in value, f(x) decreases in value.
b) As x decreases in value, f(x) increases in value. As x increases in value, f(x) decreases in value.
c) As x decreases in value, f(x) decreases in value. As x increases in value, f(x) increases in value.
d) As x decreases in value, f(x) increases in value. As x increases in value, f(x) increases in value.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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
As x decreases in value, f(x) increases in value. As x increases in value, f(x) decreases in value.
So the answer is Choice B)
Here's a graph to visually verify things.
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