Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \) \( f(x)=\operatorname{In}(x+3)-2 \) Select the correct choice helow and, if necessary, fill in the answer box to complete your choice. A. The function \( f \) is concave upward on the subinterval(s) (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) Select the correct choice beluw and, if necessary, fill in the answer box to complete your choice. A. The funclion \( f \) is concave downward on the subinterval(s) ( \( -3, \infty) \). . . (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) B. The function \( f \) is never concave downward. Select the cortect choice below and, if necessary, fill in the answer box to complete your choice. A. The function \( f \) has an inflection point at \( x= \) B. The B. The function I has no inflection point.

It seems that I am unable to plot the graph directly. However, I can describe how to sketch the graph of \( f(x) = \ln(x + 3) - 2 \): 1. **Identify the key points**: - The function has a vertical asymptote at \( x = -3 \). - The function passes through the point \( (-3, -2) \) (though it does not actually reach this point since it is undefined there). - As \( x \) approaches \( -3 \) from the right, \( f(x) \) approaches \( -2 \). - As \( x \) increases, \( f(x) \) increases without bound. 2. **Shape of the graph**: - The graph will start just above \( (-3, -2) \) and will rise to the right. - The graph will be concave downward throughout its domain. 3. **Behavior at the ends**: - As \( x \to -3^+ \), \( f(x) \to -2 \). - As \( x \to \infty \), \( f(x) \to \infty \). ### Summary of the Graph: - The graph starts from just above \( (-3, -2) \) and rises to the right, showing a concave downward shape. - There are no inflection points, and the function is concave downward for all \( x > -3 \). If you need further assistance or a specific aspect of the graph explained, feel free to ask!