Summarize the pertinent intormalion ohtained by appying the grapting stlategy and skelch the graph of \( y=f(x) \). \[ f(x)=\ln (x+8)-1 \] Select the corred choice below and, if necessary, fill in the enswer box to complete your choice. A. The \( y \)-intercept ol I is \( y=\ln (8)-1 \) (Typo an exact answer. Use a comma to separate answers as neoded.) B. The function i has no \( y \)-inlercept Select the corred choice below and, if necessary, fil in the answar box to complele vour choice. A. The function \( f \) is increasing on the subinlerval(s) \( (-8, \infty) \) (Type your answer in inferval notatiun. Use a comma to sepatale answers as needed) B. The function \( \mid \) is never increasing. Select the corred choice below and, if necessary, fill in the answer box to completo your choice. A. The function \( f \) is docreasing on the subinterval(s) \( \square \) \( \square \). (Type your answer in interval nolation (Ise a cormma to separato answers as needod.) B. The function fis never decreasing.

To find the \( y \)-intercept of the function \( f(x) = \ln(x + 8) - 1 \), we evaluate \( f(0) \). This gives us \( f(0) = \ln(8) - 1 \). Hence, the correct choice for the \( y \)-intercept is A. The \( y \)-intercept is \( y = \ln(8) - 1 \). The function \( f(x) = \ln(x + 8) - 1 \) is increasing on the interval \( (-8, \infty) \) because the derivative \( f'(x) = \frac{1}{x + 8} \) is positive for all \( x > -8 \). So, the correct choice is A. The function \( f \) is increasing on the subinterval(s) \( (-8, \infty) \). Since the function is increasing on the interval \( (-8, \infty) \), it is never decreasing. Therefore, the correct choice would be B. The function \( f \) is never decreasing. Fun Fact: Did you know that the natural logarithm, \( \ln(x) \), has its roots connected to the concept of growth? It’s a go-to model in many fields, from finance to biology, representing exponential growth or decay! If you're intrigued, pick up "The Joy of x" by Steven Strogatz, which dives into the beauty of mathematics and its real-world applications with a relatable touch. It might just spark a newfound love for logarithms!