Using limits, the correct statement is given by:
The degree is odd and the leading coefficient is negative.
It is found by it's limits as x goes to infinity. On the left, it is given by:
[tex]\lim_{x \rightarrow -\infty} f(x)[/tex]
On the right, it is given by:
[tex]\lim_{x \rightarrow \infty} f(x)[/tex]
Since it is a limit as x goes to infinity, we only consider the term with the highest degree and it's leading coefficient.
Hence, the behavior described, that is, [tex]\lim_{x \rightarrow -\infty} = \infty, \lim_{x \rightarrow \infty} = -\infty[/tex] happens when:
The degree is odd and the leading coefficient is negative.
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Answer:
The degree is odd and the leading coefficient is negative.
Step-by-step explanation:
