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To evaluate \( g(f(-5)) \), we need to follow these steps:

1. **Find \( f(-5) \) from the \( y = f(x) \) graph.**
   - At \( x = -5 \), the graph shows that \( f(-5) = -8 \).

2. **Use the result from step 1 to find \( g(-8) \) from the \( y = g(x) \) graph.**
   - At \( x = -8 \), the \( y = g(x) \) graph shows that \( g(-8) = 4 \).

Thus, \( g(f(-5)) = 4 \).

Would you like more details or have any questions about this solution? 

Here are some related questions for further exploration:
1. How do you evaluate \( f(g(-3)) \) using the graphs?
2. What happens to the composition \( g(f(x)) \) when \( x = 0 \)?
3. How do you determine the range of \( g(f(x)) \) over the interval \( -10 \leq x \leq 10 \)?
4. How do you find \( g(f(2)) \) using the graphs?
5. What is the inverse of the function \( f \) or \( g \), if they exist?

**Tip:** When evaluating composite functions like \( g(f(x)) \), always start with the inner function.

Learn how to evaluate the composite function g(f(-5)) using graph interpretation. Follow a step-by-step solution involving function evaluation from graphs of y = f(x) and y = g(x). This problem focuses on understanding composite functions and is suitable for students in Grades 9-11.

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