Using limits, the correct option regarding the end behavior of the function is given by:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
The end behavior is found calculating the limit of f(x) as x goes to infinity.
For this problem, the equation is given by:
[tex]f(x) = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108[/tex]
Since x goes to infinity, we consider only the term with the highest exponent, hence the limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow -\infty} -x^6 = -(-\infty)^6 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow \infty} -x^6 = -(\infty)^6 = -\infty[/tex]
Hence the correct option is:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
More can be learned about limits and end behavior at https://brainly.com/question/22026723
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