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To evaluate \( g(f(-9)) \), let's start by finding \( f(-9) \) using the graph of \( y = f(x) \):

1. On the graph of \( y = f(x) \), locate \( x = -9 \).
2. From the graph, the point \( (-9, f(-9)) \) corresponds to \( y = 3 \). So, \( f(-9) = 3 \).

Next, we find \( g(3) \) using the graph of \( y = g(x) \):

1. On the graph of \( y = g(x) \), locate \( x = 3 \).
2. From the graph, the point \( (3, g(3)) \) corresponds to \( y = -4 \). So, \( g(3) = -4 \).

Therefore, \( g(f(-9)) = g(3) = -4 \).

Would you like any more details on this process, or do you have any other questions?

**Here are some related questions you might consider:**
1. What is the domain and range of the function \( f(x) \)?
2. What is the domain and range of the function \( g(x) \)?
3. How would you evaluate \( f(g(0)) \)?
4. Can you determine the intersection points of the graphs of \( f \) and \( g \)?
5. What are the x-intercepts and y-intercepts for each function?

**Tip:** When evaluating composite functions from graphs, always ensure you read the graph accurately and confirm your initial findings to avoid simple mistakes.

This problem involves evaluating the composite function g(f(-9)) using the graphs of f(x) and g(x). Step-by-step, it finds f(-9) from the graph of f(x) and then uses this value to determine g(f(-9)) from the graph of g(x). This example covers key concepts like composite functions and graph interpretation, suitable for students in Grades 9-12.

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