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URGENT!!! What happens to the graph of y=−x6−6x5+50x3+45x2−108x−108 as x heads toward ∞ and −∞?
A. as x→∞, y→−∞ as x→−∞, y→−∞
B. as x→∞, y→∞ as x→−∞, y→∞
C. as x→∞, y→∞ as x→−∞, y→−∞
D. as x→∞, y→−∞ as x→−∞, y→∞

Respuesta :

Using limits, the correct option regarding the end behavior of the function is given by:

A. as x→∞, y→−∞ as x→−∞, y→−∞.

How to find the end behavior of a function f(x)?

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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