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We want to determine the end behavior of the graph of the given polynomial function. To do so, we will pay close attention to the leading term $ax_{n},$ where $a$ is the leading coefficient and $n$ is the degree of the polynomial. Let's first rewrite the given polynomial function in standard form.
$f(x)=8x_{5}−4x_{7}+6x_{2}⇔f(x)=-4x_{7}+8x_{5}+6x_{2} $
We can see above that the leading coefficient is $-4$ and the degree is $7.$ Let's now see how the leading coefficient and degree affect the end behavior of the graph of a polynomial function.

$a>0,$ $neven$

$a>0,$ $nodd$

$a<0,$ $neven$

$a<0,$ $nodd$

$Reset$

Since $-4<0$ and $7$ is an odd number, the end behavior of the given function is **up** and **down.**
We can see above that as $x$ approaches negative infinity, $f(x)$ approaches positive infinity. As $x$ approaches positive infinity, $f(x)$ approaches negative infinity.
$f(x)→+∞asx→-∞andf(x)→-∞asx→+∞ $