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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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 consider the given polynomial function. Note that it is already written in standard form. $f(x)=5x_{7}+11x_{4}−7x_{2}−4x−17 $ We can see above that the leading coefficient is $5$ 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 $5>0$ and $7$ is an odd number, the end behavior of the given function is **down** and **up.**
$f(x)→-∞f(x)→∞ asas x→-∞x→∞ $