(c) $g(x)=\frac{6 x^{3}}{x^{2}-2 x-8}$ V.A.'s: H.A.: tional function. $\frac{x^{2}-4}{x^{2}+2 x+1}$ (c) $g(x)=\frac{x^{2}-6 x+9}{x^{2}+5 x}$ $x$-int.'s: $y$-int.: 2 Summer 2023

Step 1 ：The function given is \(g(x)=\frac{6 x^{3}}{x^{2}-2 x-8}\).

Step 2 ：The vertical asymptotes of the function are found by setting the denominator equal to zero and solving for x. This gives us \(x=-2\) and \(x=4\).

Step 3 ：The horizontal asymptote of the function is found by comparing the degrees of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, the function has a horizontal asymptote at \(y=\infty\).

Step 4 ：The x-intercept of the function is found by setting the numerator equal to zero and solving for x. This gives us \(x=0\).

Step 5 ：The y-intercept of the function is found by setting \(x=0\) in the function. This gives us \(y=0\).

Step 6 ：So, the final answer is \(\boxed{x=-2, x=4, y=\infty, x=0, y=0}\).