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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. Let's first rewrite the given polynomial function in standard form.

$f(x)=10−14x_{3}−3x_{5}−16x_{2}−5x⇕f(x)=-3x_{5}−14x_{3}−16x_{2}−5x+10 $ We can see above that the leading coefficient is $-3$ and the degree is $5.$ 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 $-3<0$ and $5$ is an odd number, the end behavior of the given function is **up** and **down.**
$f(x)→∞f(x)→-∞ asas x→-∞x→∞ $