Question

consider the polynomial function $f(n)=8n^{7}+2 - 2n^{5}$. as $n
ightarrow-infty$, $f(n)
ightarrow$ select an answer. as $n
ightarrowinfty$, $f(n)
ightarrow$ select an answer.

Explanation:

Step1: Identify the leading - term

The leading - term of the polynomial function $f(n)=8n^{7}+2 - 2n^{5}$ is $8n^{7}$ since the highest - power of $n$ is 7.

Step2: Analyze as $n\to-\infty$

When $n\to-\infty$, for the term $y = 8n^{7}$, since the exponent 7 is odd and the coefficient 8 is positive, $8n^{7}\to-\infty$ as $n\to-\infty$. So $f(n)\to-\infty$ as $n\to-\infty$.

Step3: Analyze as $n\to\infty$

When $n\to\infty$, for the term $y = 8n^{7}$, since the exponent 7 is odd and the coefficient 8 is positive, $8n^{7}\to\infty$ as $n\to\infty$. So $f(n)\to\infty$ as $n\to\infty$.

Answer:

As $n\to-\infty$, $f(n)\to-\infty$; As $n\to\infty$, $f(n)\to\infty$