Question 5 Describe the long run behavior of $$ f(n)=n^{9}+3 n^{7}-5 n^{5}-2 $$ As $$ n \rightarrow-\infty, f(n) \rightarrow ? \vee $$ As $$ n \rightarrow \infty, f(n) \rightarrow ? \vee $$ Question Help: $$ \square $$ Video Submit Question

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$f(n)$ approaches negative infinity as $n$ approaches negative infinity and approaches positive infinity as $n$ approaches positive infinity. As $n$ approaches negative infinity, all the terms in $f(n)$ become very large negative numbers, since $n^9$ and $n^7$ grow much faster than $n^5$ and $2$ is a small constant. Therefore, $f(n)$ approaches negative infinity as $n$ approaches negative infinity. As $n$ approaches positive infinity, the terms $n^9$ and $3n^7$ dominate, and $f(n)$ grows without bound. Therefore, $f(n)$ approaches positive infinity as $n$ approaches positive infinity. In summary, as $n$ approaches negative infinity, $f(n)$ approaches negative infinity, and as $n$ approaches positive infinity, $f(n)$ approaches positive infinity.

Question 5 Describe the long run behavior of \( f(n)=n^{9}+3 n^{7}-5 n^{5}-2 \) As \( n \rightarrow-\infty, f(n) \rightarrow ? \vee \) As \( n \rightarrow \infty, f(n) \rightarrow ? \vee \) Question Help: \( \square \) Video Submit Question

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Question 5 Describe the long run behavior of \( f(n)=n^{9}+3 n^{7}-5 n^{5}-2 \) As \( n \rightarrow-\infty, f(n) \rightarrow ? \vee \) As \( n \rightarrow \infty, f(n) \rightarrow ? \vee \) Question Help: \( \square \) Video Submit Question

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