Summarize the pertinent information oblained by applying the graphing stralegy and skelch the graph of .

Select the cortect choice below and, if necessary, fill in the answer box to complole your chrica.
A. The domain of is .
(Type your answer in interval notation. Uso a comma to separate answers as neaded.)
B. The domain of 1 is empty.

Ask by Hall Burns. in the United States

Mar 11,2025

Question

Summarize the pertinent information oblained by applying the graphing stralegy and skelch the graph of .

Select the cortect choice below and, if necessary, fill in the answer box to complole your chrica.
A. The domain of is .
(Type your answer in interval notation. Uso a comma to separate answers as neaded.)
B. The domain of 1 is empty.

Ask by Hall Burns. in the United States

Mar 11,2025

UpStudy AI · Accepted Answer

1. Given the function  
   $$
   f(x)=\ln(x+8)-1,
   $$  
   we first identify the restrictions from the logarithm. Since the natural logarithm is defined only when its argument is positive, we require  
   $$
   x+8>0.
   $$

2. Solving the inequality, we subtract 8 from both sides:  
   $$
   x > -8.
   $$

3. Therefore, the domain of $$ f $$ in interval notation is  
   $$
   (-8,\infty).
   $$

4. In addition to the domain, note these few facts about the function:  
   - The expression $$ x+8 $$ means there is a horizontal shift of 8 units to the left relative to $$ \ln x $$.  
   - The $$-1$$ represents a vertical shift downward by 1 unit.  
   - There is a vertical asymptote at $$ x = -8 $$.

5. Based on the choices provided, the correct selection is:  
   **A. The domain of $$ f $$ is $$(-8,\infty)$$.**
A. The domain of $$ f $$ is $$(-8,\infty)$$.

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