Answer
graph IV
Work Step by Step
The end behavior of U(x) matches the end behavior of the leading term, $-x^{3}.$
As $x\rightarrow-\infty,$
$x^{3} $is a large negative number,
$-x^{3} $is a large positive number,
$U$(x)$\rightarrow$+$\infty$
(the graph rises up on the far left)
As $x\rightarrow+\infty,$
$x^{3} $is a large positive number,
$-x^{3} $is a large negative number,
$U$(x)$\rightarrow-\infty$
(the graph sinks down on the far right)
Graphs that fit this behavior are IV and V.
To decide, calculate U(1)=-1+2, (positive)
which makes our choice:
graph IV
