Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( f(x)=\frac{x+9}{x-9} \). Find the location of any local extrema of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. There is a local maximum at \( x=\square \). There is no local minimum. (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There is a local minimum at \( x=\square \). There is no local maximum. (Type an integer or a decimal. Use a comma to separate answers as needed.) C. There is a local maximum at \( x=\square \) and there is a local minimum at \( x=\square \). (Type integers or decimals. Use a comma to separate answers as needed.) D. There are no local extrema.

To analyze the function \( f(x) = \frac{x+9}{x-9} \), we begin by identifying key features through its graph. This function exhibits a vertical asymptote at \( x=9 \) and a horizontal asymptote at \( y=1 \). As \( x \) approaches 9 from the left, \( f(x) \) approaches negative infinity and from the right, it approaches positive infinity. The function crosses the y-axis at \( f(0) = -1 \), creating a clear S-shape graph. To find local extrema, we check the critical points by taking the derivative \( f'(x) \) and setting it to zero. Upon differentiating, we find that \( x = -9 \) is the only critical point. Evaluating the second derivative reveals this critical point corresponds to a local minimum. Thus, we conclude: B. There is a local minimum at \( x=-9 \). There is no local maximum.