Answer
graph III
Work Step by Step
As $x\rightarrow-\infty,$
x is a large negative number
$x^{2} $ is a large positive number, and so is $(x^{2}-4)$
Their product is negative.
So as $ x\rightarrow-\infty$, P(x)$\rightarrow-\infty$
(the graph sinks down on the far left)
As $x\rightarrow+\infty,$
x is a large positive number
$x^{2} $ is a large positive number, and so is $(x^{2}-4)$
Their product is positive.
So as $ x\rightarrow$+$\infty$, P(x)$\rightarrow$+$\infty$
(the graph rises up on the far right)
The graph that fits this behavior is
graph III
