Question

f(x)=-392 + 399x-7x^{3}
answer attempt 2 out of 2
the degree of the polynomial is even, and the leading coefficient is positive
choose which pair of limits below represents the end - behavior:
\\(\lim_{x\to - \infty}f(x)=\infty, \lim_{x\to\infty}f(x)=\infty\\)
\\(\lim_{x\to - \infty}f(x)=-\infty, \lim_{x\to\infty}f(x)=\infty\\)
\\(\lim_{x\to - \infty}f(x)=\infty, \lim_{x\to\infty}f(x)=-\infty\\)
\\(\lim_{x\to - \infty}f(x)=-\infty, \lim_{x\to\infty}f(x)=-\infty\\)

Explanation:

Step1: Identify degree and leading - coefficient

The polynomial $f(x)=-392 + 399x-7x^{3}$ has degree $n = 3$ (odd) and leading coefficient $a=-7$ (negative).

Step2: Recall end - behavior rules

For a polynomial $y = a_nx^n+\cdots+a_0$ with odd degree $n$ and negative leading coefficient $a_n$: as $x\to-\infty$, $y\to\infty$; as $x\to\infty$, $y\to-\infty$. That is $\lim_{x\to-\infty}f(x)=\infty$ and $\lim_{x\to\infty}f(x)=-\infty$.

Answer:

$\lim_{x\to-\infty}f(x)=\infty,\lim_{x\to\infty}f(x)=-\infty$