Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( f(x)=\frac{x+3}{x-3} \) Find the intervals where \( f(x) \) is concave upward or downward. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The function is concave upward on is concave downward on . It is never concave downward. It is never concave upward. C. The function is concave upward on Find the location of any in concave downward on A. There is an inflection points of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no inflection points.

To graph the function \( f(x) = \frac{x+3}{x-3} \), start by identifying key features. The vertical asymptote occurs at \( x = 3 \), where the function is undefined. The horizontal asymptote can be approached as \( y = 1 \) when \( x \) approaches positive or negative infinity. Plotting points around the asymptotes, you’ll notice that the graph crosses the y-axis at \( (0, -1) \) and approaches the asymptotes on either side, creating a hyperbolic shape. Next, to determine concavity, compute the second derivative \( f''(x) \). The function is concave upward where \( f''(x) > 0 \) and concave downward where \( f''(x) < 0 \). After analyzing the sign of \( f''(x) \), you might discover that the function is concave upward on \( (-\infty, 0) \) and concave downward on \( (0, 3) \), with no intervals being never concave upward or downward. An inflection point, where the concavity changes, occurs at \( x = 0 \). So to summarize the findings: - The function is concave upward on \( (-\infty, 0) \) and concave downward on \( (0, 3) \). - There is an inflection point at \( x = 0 \).