Summarize the pertinent information oblained by applying the graphing stralegy and skelch the graph of \( y=f(x) \). \( f(x)=\ln (x+8)-1 \) Select the cortect choice below and, if necessary, fill in the answer box to complole your chrica. A. The domain of \( f \) is \( \square \). (Type your answer in interval notation. Uso a comma to separate answers as neaded.) B. The domain of 1 is empty.

The function \( f(x) = \ln(x+8) - 1 \) depends on the logarithm, which requires that the argument \( x + 8 \) be greater than zero. This means that \( x + 8 > 0 \) or \( x > -8 \). Therefore, the domain of \( f \) is all real numbers greater than \(-8\), which can be expressed in interval notation as \( (-8, \infty) \). To sketch the graph of \( f(x) \), start by marking the vertical asymptote at \( x = -8 \), where the function approaches negative infinity. As \( x \) increases, \( f(x) \) rises gradually, crossing the y-axis at \( f(0) = \ln(8) - 1 \). The curve continues to grow indefinitely, illustrating the properties of logarithmic growth.