Answer
graph (c)
Work Step by Step
The Leading Coefficient Test (page 350):
As $x$ increases or decreases without bound, the graph of
$f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+ \cdot\cdot\cdot +a_{1}x+a_{0} (a_{n}\neq 0)$
eventually rises or falls. In particular,
l. For $n$ odd:
If the leading coefficient is positive,
the graph falls to the left and rises to the right $a_{n}>0 (\swarrow,\nearrow)$.
If the leading coefficient is negative,
the graph is negative, the graph rises to the left and falls to the right. $a_{n}<0 (\nwarrow,\searrow)$
2. For $n$ even:
If the leading coefficient is positive,
the graph rises to the left and rises to the right. $a_{n}>0 (\nwarrow,\nearrow)$
If the leading coefficient is negative,
the graph falls to the left and falls to the right. $a_{n}<0 (\swarrow, \searrow)$
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For this function,
$n$ is odd, leading coefficient is negative,
we look for behavior: $(\nwarrow,\searrow)$ ,
to which the closest is
graph (c)
