https://file.aiquickdraw.com/mathbot/file/172945274438294zfvn72.jpg

### Solution:

Let's analyze the graph and respond to the two questions regarding **domain** and **range**:

1. **Domain:**
   The domain represents the values of \( w \) (weeks) for which the function \( f(w) \) is defined. From the graph, the function starts at \( w = 0 \) and ends at \( w = 16 \) (this is where the function reaches \( I = 0 \), implying the end of the epidemic). Thus, the domain is:
   \[
   \text{Domain: } [0, 16]
   \]
   This means the epidemic is tracked for a period of 16 weeks.

2. **Range:**
   The range represents the possible values of \( I \) (number of infected individuals in thousands) based on the graph. The graph shows that \( I \) starts at 0, reaches a maximum of approximately 8,000 individuals, and then returns to 0 by week 16. Hence, the range is:
   \[
   \text{Range: } [0, 8]
   \]
   This means the number of infected individuals varies from 0 to 8 thousand during the course of the epidemic.

### Interpretation:

- **Domain Interpretation:** The domain tells us the duration of the epidemic, which lasts for 16 weeks. The epidemic starts at week 0 and is fully over by week 16.
  
- **Range Interpretation:** The range tells us how many people are infected at any given time. The number of infections starts at 0, peaks at 8,000 infected individuals (around week 6), and then gradually declines back to 0 by the end of the 16 weeks. This shows the rise and fall of the epidemic.

Would you like any additional details or clarification?

### Related Questions:

1. How would the domain change if the epidemic lasted longer than 16 weeks?
2. What does it mean if the graph never reaches 0 again at the end?
3. How would we describe the domain and range if the number of infected individuals kept increasing beyond 8,000?
4. What other factors might influence the shape of the curve in real-world epidemics?
5. How would the domain and range change if we tracked infections for a smaller city?

### Tip:
When analyzing graphs, always look for key turning points (like maximums and minimums) to help determine the range and the overall behavior of the function.

An epidemic of influenza spreads through a city. The figure shows a graph of I = f(w), where I is the number of individuals (in thousands) infected w weeks after the epidemic begins. Calculate the domain and range for this function. What does the domain and range tell us in this function? Explain applied to this scenario.

Analyze the domain and range of a function representing an influenza epidemic. This problem uses a real-world graph to explain how to determine the period of an epidemic and how many individuals are infected over time. Suitable for students in Grades 9-12.

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