Using limits, it is found that the statement that best describes the end behavior of [tex]f(x) = 9 - 3x - 4x^4 + 2x^3[/tex] is:
[tex]As x \rightarrow \pm \infty, f(x) \rightarrow \pm -\infty[/tex]
How to find the end behavior of a function?
The end behavior of a function is given by it's limits as x goes to infinity.
In this problem, the function is given by:
[tex]f(x) = 9 - 3x - 4x^4 + 2x^3[/tex]
Hence the limits are, considering only the highest exponent as x goes to infinity:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} - 4x^4 = -4(-\infty)^4 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} - 4x^4 = -4(\infty)^4 = -\infty[/tex]
Hence, the statement is:
[tex]As x \rightarrow \pm \infty, f(x) \rightarrow \pm -\infty[/tex]
More can be learned about limits at https://brainly.com/question/22026723
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