Answer :
Final answer:
The end behavior of the given function is that it approaches negative infinity as x approaches negative infinity, and approaches positive infinity as x approaches positive infinity.
Explanation:
The end behavior of a function describes what happens to the function as the input values become very large or very small.
In this case, we have the function [tex]y = 4x^9 + 6x^6 + 6x^5 + 3.[/tex]
As x approaches negative infinity, all the terms in the function become negative, except for the constant term 3. Therefore, the function will approach negative infinity.
As x approaches positive infinity, all the terms in the function become positive, and the highest degree term [tex]4x^9[/tex]dominates the function. Therefore, the function will approach positive infinity.
Thus, the end behavior of the given function is that it approaches negative infinity as x approaches negative infinity, and approaches positive infinity as x approaches positive infinity.
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