https://file.aiquickdraw.com/mathbot/file/1728312404512i5mvnemm.jpg

The graph depicts the population of Detroit (in thousands) over time, specifically the years since 1970. To determine whether this graph represents a function, we apply the **vertical line test**. If any vertical line drawn through the graph intersects the curve at more than one point, it is not a function. 

In this case, for every value of "Years since 1970" (on the horizontal axis), there is only one corresponding population value (on the vertical axis). Therefore, the graph passes the vertical line test and represents a function.

So, the correct answer is **Yes**.

Would you like more details on how the vertical line test works or have any questions? Here are some related questions to explore further:

1. What is the vertical line test in more detail?
2. Can you explain how functions relate to real-world scenarios like population trends?
3. What are some examples of graphs that would not represent functions?
4. How does the concept of "one output for each input" define a function?
5. How can we mathematically describe this population trend?

**Tip:** When analyzing a graph, always check for uniqueness of output values (y-values) for each input (x-value) to determine if it represents a function.

Analyze whether the graph of Detroit's population over years represents a function by applying the vertical line test. The problem involves function analysis and graph interpretation, suitable for students in Grades 7-10.

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