https://file.aiquickdraw.com/mathbot/file/1728597028740i4azmus9.jpg

Let's evaluate the two expressions step by step using the provided table.

1. **For \( f(g(-3)) \):**
   - First, find \( g(-3) \). According to the table, \( g(-3) = -1 \).
   - Next, find \( f(-1) \). From the table, \( f(-1) = 2 \).

   So, \( f(g(-3)) = f(-1) = 2 \).

2. **For \( g(f(4)) \):**
   - First, find \( f(4) \). According to the table, \( f(4) = -3 \).
   - Next, find \( g(-3) \). From the table, \( g(-3) = -1 \).

   So, \( g(f(4)) = g(-3) = -1 \).

### Final Results:
- \( f(g(-3)) = 2 \)
- \( g(f(4)) = -1 \)

Would you like more details or have any questions? Here are some related questions you can explore:

1. How do you compose functions like \( f(g(x)) \) for different values of \( x \)?
2. Can you explain why composing functions involves applying one function after the other?
3. How would you evaluate \( g(g(-3)) \) using the table?
4. How do function tables help in understanding function composition?
5. Can you find \( f(f(5)) \) using the table?

**Tip:** When composing functions, always start with the innermost function and work outward.

Use the table below to evaluate f(g(-3)) and g(f(4)).

Learn how to evaluate the composite functions f(g(-3)) and g(f(4)) using a table of function values. This problem demonstrates key concepts of function composition and provides a step-by-step solution using algebraic methods. Suitable for students in Grades 9-10.

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