Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( f(x)=\frac{8 x}{x^{2}-4} \). Find the domain of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is all real \( x \), except \( x= \) \( \square \) (Type an integer or a decimal. Use a comma to separate answers as needed.) B. The domain is all real \( x \). Find the \( x \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( x \)-intercept(s) is/are at \( x= \) \( \square \) (Type an integer or a decimal Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts. Find the \( y \)-intercepts of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept(s) is/are at \( y= \) \( \square \) (Type an integer or a decimal. Use a comma to separate answers as needed.)

To find the domain of \( f(x)=\frac{8 x}{x^{2}-4} \), we need to identify the values of \( x \) that make the denominator zero. The expression \( x^2 - 4 = 0 \) gives \( x = 2 \) and \( x = -2 \). Therefore, the domain is all real \( x \), except \( x = -2 \) and \( x = 2 \). A. The domain is all real \( x \), except \( x= \) \( -2, 2 \). Next, to find the \( x \)-intercepts, we set \( f(x) = 0 \). The numerator \( 8x = 0 \) gives \( x = 0 \). Thus, there is one \( x \)-intercept at \( x = 0 \). A. The \( x \)-intercept(s) is/are at \( x= \) \( 0 \). For the \( y \)-intercept, we find \( f(0) \) by substituting \( x = 0 \) into the function. This results in \( f(0) = \frac{8(0)}{0^2 - 4} = 0 \). Therefore, the \( y \)-intercept is also at \( y = 0 \). A. The \( y \)-intercept(s) is/are at \( y= \) \( 0 \). Now, sketching the graph, we see that it has vertical asymptotes at \( x = -2 \) and \( x = 2 \), an \( x \)-intercept at \( (0, 0) \), and a \( y \)-intercept also at \( (0, 0) \). The graph approaches the asymptotes but does not touch them, demonstrating the classic behavior of rational functions with vertical asymptotes.