Question

the function $f(x)$ is defined below. what is the end - behavior of $f(x)$?
$f(x)=480 - 224x-264x^{2}+8x^{4}$
answer attempt 1 out of 1
the degree of the polynomial is, and the leading coefficient is
choose which pair of limits below represents the end - behavior:
$lim_{x
ightarrow-infty}f(x)=infty,lim_{x
ightarrowinfty}f(x)=infty$
$lim_{x
ightarrow-infty}f(x)=-infty,lim_{x
ightarrowinfty}f(x)=infty$
$lim_{x
ightarrow-infty}f(x)=infty,lim_{x
ightarrowinfty}f(x)=-infty$
$lim_{x
ightarrow-infty}f(x)=-infty,lim_{x
ightarrowinfty}f(x)=-infty$

Explanation:

Step1: Identify degree and leading - coefficient

For the polynomial $f(x)=480 - 224x-264x^{2}+8x^{4}$, the degree $n = 4$ (the highest power of $x$) and the leading coefficient $a = 8$ (the coefficient of $x^{4}$).

Step2: Determine end - behavior rules

For a polynomial $y = a x^{n}$, when $n$ is even and $a>0$, $\lim_{x
ightarrow-\infty}f(x)=\infty$ and $\lim_{x
ightarrow\infty}f(x)=\infty$.

Answer:

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