Graph the following function. Based on the graph, state the domain and the range and find any intercepts. $$ f(x)=\left\{\begin{array}{l}-\ln \frac{x}{2} ext { if } 00\} $$. (Simplify your answer. Use a comma to separate answers as needed.) B. The domain is $$ \{x \mid x \leq, x
eq \square $$ (Simplify your answer. Use a comma to separate answers as needed.) C. The domain is $$ \{x \mid x \geq $$, $$ x
eq $$, $$ \} $$. (Simplify your answer. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers. The range of the function $$ f(x) $$ is $$ \square $$. (Type your answer in interval notation.)

Question

Graph the following function. Based on the graph, state the domain and the range and find any intercepts. $$ f(x)=\left\{\begin{array}{l}-\ln \frac{x}{2} 	ext { if } 00\} $$. (Simplify your answer. Use a comma to separate answers as needed.) B. The domain is $$ \{x \mid x \leq, x 
eq \square $$ (Simplify your answer. Use a comma to separate answers as needed.) C. The domain is $$ \{x \mid x \geq $$, $$ x 
eq $$, $$ \} $$. (Simplify your answer. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers. The range of the function $$ f(x) $$ is $$ \square $$. (Type your answer in interval notation.)

UpStudy AI · Accepted Answer

The function is defined piecewise as

$$
f(x)=\begin{cases}
-\ln\left(\dfrac{x}{2}\right) & \text{if } 00$$ (the logarithm is defined only for positive arguments), the overall domain is

\[
\{x \mid x>0\}.
$$

Thus, the correct choice is **A. The domain is $$\{x \mid x>0\}$$.**

**Step 2. Determine the Range**

*For $$00\}$$
- **Range:** $$[0, +\infty)$$
**Domain:** $$ \{x \mid x > 0\} $$ **Range:** $$[0, +\infty)$$ **Intercepts:** - **x-intercept:** $$(2, 0)$$ - **No y-intercept**

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