Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( y=f(x) \). \( f(x)=\ln (x+3)-2 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of \( f \) is (lype your answer in interval notation. Use a comma to separate answers as needed.) B. The domain of \( f \) is empty.

To determine the domain of the function \( f(x) = \ln(x+3) - 2 \), we must find the values of \( x \) for which the logarithm is defined. The argument of the logarithm, \( x + 3 \), must be greater than zero, leading us to: \[ x + 3 > 0 \] Solving this gives: \[ x > -3 \] Thus, the domain of \( f \) in interval notation is \( (-3, \infty) \). Next, let's sketch the graph. The function has a vertical asymptote at \( x = -3 \) and approaches \( y = -2 \) as \( x \) increases. The graph will increase from the asymptote and steadily rise towards positive infinity. So, to fill in the answer box for A, the domain of \( f \) is: **(-3, ∞)**.