Answer
graph II
Work Step by Step
The end behaviour of S(x) matches the end behavior of the leading term, $\displaystyle \frac{1}{2}x^{6}.$
As $x\rightarrow-\infty,$
$x^{6}$ is a large positive number,
$\displaystyle \frac{1}{2}x^{6}$ is a large positive number
S(x)$\rightarrow$+$\infty$
(the graph rises up on the far left)
As $ x\rightarrow$+$\infty,$
$x^{6}$ is a large positive number,
$\displaystyle \frac{1}{2}x^{6}$ is a large positive number
S(x)$\rightarrow$+$\infty$
(the graph rises up on the far right)
Graphs that fit this behavior are II and VI.
To decide, calculate S(1)=$\displaystyle \frac{1}{2}-2$, (negative)
which makes our choice:
graph II
