# How do you find the end behavior of #f(x) = -x^(4) + 6x^(3) - 9^(2)#?

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End behaviour is determined by the leading coefficient and the degree.

Here degree is even and the leading coefficient negative, hence the graph will fall to the right and fall to the left.

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To find the end behavior of ( f(x) = -x^4 + 6x^3 - 9x^2 ), observe the leading term of the polynomial, which is ( -x^4 ).

As ( x ) approaches positive infinity, ( -x^4 ) approaches negative infinity.

As ( x ) approaches negative infinity, ( -x^4 ) approaches negative infinity.

Therefore, the end behavior of the function ( f(x) = -x^4 + 6x^3 - 9x^2 ) is that as ( x ) approaches positive or negative infinity, ( f(x) ) approaches negative infinity.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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