Answer
graph V
Work Step by Step
The end behaviour of R(x) matches the end behavior of the leading term, $-x^{5}$
As $x\rightarrow-\infty,$
$x^{5}$ is a large negative number,
$-x^{5} $ is a large positive number, so
as $x\rightarrow-\infty,$ R(x)$\rightarrow$+$\infty$
(the graph rises up on the far left)
As $ x\rightarrow$+$\infty,$
$x^{5}$ is a large positive number,
$-x^{5} $ is a large negative number, so
as $x\rightarrow+\infty,$ R(x)$\rightarrow-\infty$
(the graph sinks down on the far right)
The graphs that fit this behavior are IV and V.
To decide, calculate R(1)=$-1+5-4=0$,
so we choose the graph whose x-intercept is 1,
graph V
