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.