# What is the end behavior of the graph of #f(x)=-2x^4+7x^2+4x-4#?

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The end behavior of the graph of ( f(x) = -2x^4 + 7x^2 + 4x - 4 ) can be determined by observing the leading term of the polynomial function, which is ( -2x^4 ).

As ( x ) approaches positive infinity (( +\infty )), the leading term ( -2x^4 ) dominates the behavior of the function. Since the leading coefficient is negative and the exponent of ( x ) is even, the end behavior of the graph is as follows:

- As ( x ) approaches positive infinity, ( f(x) ) approaches negative infinity (( -\infty )).

Similarly, as ( x ) approaches negative infinity (( -\infty )), the leading term ( -2x^4 ) dominates the behavior of the function. Again, since the leading coefficient is negative and the exponent of ( x ) is even, the end behavior of the graph is as follows:

- As ( x ) approaches negative infinity, ( f(x) ) approaches negative infinity (( -\infty )).

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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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