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 axn, 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)=5x7+11x4−7x2−4x−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.
Since 5>0 and 7 is an odd number, the end behavior of the given function is down and up. f(x)→-∞f(x)→∞asasx→-∞x→∞