https://file.aiquickdraw.com/mathbot/file/17259244067110qf3wgk0.jpg

Let's evaluate the expressions using the given graphs for \( f(x) \) and \( g(x) \).

### 1. \( g(f(0)) \)
- First, find \( f(0) \) from the graph of \( f(x) \). Looking at the graph, \( f(0) = -2 \).
- Now, find \( g(-2) \) from the graph of \( g(x) \). From the graph, \( g(-2) = 2 \).
- So, \( g(f(0)) = g(-2) = 2 \).

### 2. \( f(f(-3)) \)
- First, find \( f(-3) \) from the graph of \( f(x) \). Looking at the graph, \( f(-3) = 0 \).
- Now, find \( f(0) \). From the graph of \( f(x) \), \( f(0) = -2 \).
- So, \( f(f(-3)) = f(0) = -2 \).

### Final Answers:
1. \( g(f(0)) = 2 \)
2. \( f(f(-3)) = -2 \)

If you have any questions or need further details, feel free to ask!

Here are 5 related questions:
1. How do you determine the value of \( f(x) \) from a graph?
2. What is the difference between evaluating \( f(x) \) and \( g(x) \)?
3. Can you explain what it means to compose two functions, such as \( f(g(x)) \)?
4. How does the behavior of linear functions differ from non-linear ones on graphs?
5. What are the key points to check when finding values of composed functions?

**Tip:** When dealing with function composition, always evaluate the innermost function first, then use that result to evaluate the outer function.

Function composition using graphs: f(g(-6)), g(f(0)), f(f(-3)), g(g(-5)).

Learn how to solve function composition problems using graphs for f(x) and g(x). This problem explores function composition, including evaluating expressions like g(f(0)) and f(f(-3)) with step-by-step solutions. Suitable for students in Grades 8-10.

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