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Answer :
Final answer:
The end behavior of the function f(x) = -4x^10 + 3x^5 - 45 is that it approaches negative infinity as x approaches both positive and negative infinity.
Explanation:
To describe the end behavior of the function f(x) = -4x^10 + 3x^5 - 45, we need to look at the leading term, which in this case is -4x^10. Since the coefficient of the leading term is negative and the power is even, as x approaches infinity, f(x) will approach negative infinity. Similarly, as x approaches negative infinity, f(x) will also approach negative infinity due to the even power. Therefore, the end behavior of the function can be summarized as follows: both ends of the graph point downwards.
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