Choose the end behavior of the graph of each polynomial function. \begin{tabular}{|l|l|} \hline (a) $f(x)=4 x^{5}-9 x^{3}+6 x-3$ & Falls to the left and rises to the right \\ Rises to the left and falls to the right \\ Rises to the left and rises to the right \\ Falls to the left and falls to the right \\ (b) $f(x)=-6 x^{4}+2 x^{3}+x-5$ \\ Ralls to the left and rises to the right \\ Rises to the left and rises to the right \\ (c) $f(x)=-5 x(2 x-5)^{2}$ \\ Falis to the left and falls to the right to the left and nises to the right \\ \hline \end{tabular}

Step 1 ：The end behavior of a polynomial function is determined by the degree and the leading coefficient of the polynomial. If the degree of the polynomial is odd, and the leading coefficient is positive, the end behavior is 'Falls to the left and rises to the right'. If the degree is odd and the leading coefficient is negative, the end behavior is 'Rises to the left and falls to the right'. If the degree is even and the leading coefficient is positive, the end behavior is 'Rises to the left and rises to the right'. If the degree is even and the leading coefficient is negative, the end behavior is 'Falls to the left and falls to the right'.

Step 2 ：For the first function, \(f(x)=4 x^{5}-9 x^{3}+6 x-3\), the degree is 5 (odd) and the leading coefficient is 4 (positive), so the end behavior should be 'Falls to the left and rises to the right'.

Step 3 ：For the second function, \(f(x)=-6 x^{4}+2 x^{3}+x-5\), the degree is 4 (even) and the leading coefficient is -6 (negative), so the end behavior should be 'Falls to the left and falls to the right'.

Step 4 ：For the third function, \(f(x)=-5 x(2 x-5)^{2}\), the degree is 3 (odd) and the leading coefficient is -5 (negative), so the end behavior should be 'Rises to the left and falls to the right'.

Step 5 ：Final Answer: (a) \(f(x)=4 x^{5}-9 x^{3}+6 x-3\) : \(\boxed{\text{Falls to the left and rises to the right}}\)

Step 6 ：Final Answer: (b) \(f(x)=-6 x^{4}+2 x^{3}+x-5\) : \(\boxed{\text{Falls to the left and falls to the right}}\)

Step 7 ：Final Answer: (c) \(f(x)=-5 x(2 x-5)^{2}\) : \(\boxed{\text{Rises to the left and falls to the right}}\)