Let's go through each of the expressions step by step using the given graphs for $f(x)$ and $g(x)$.

1. $f(g(-1))$

• First, find $g(-1)$ from the graph of $g(x)$. From the graph, when $x = -1$, $g(-1) = 1$.
• Now, find $f(1)$ from the graph of $f(x)$. From the graph, when $x = 1$, $f(1) = 5$.
• Therefore, $f(g(-1)) = f(1) = 5$.

2. $g(f(0))$

• First, find $f(0)$ from the graph of $f(x)$. From the graph, when $x = 0$, $f(0) = 2$.
• Now, find $g(2)$ from the graph of $g(x)$. From the graph, when $x = 2$, $g(2) = -2$.
• Therefore, $g(f(0)) = g(2) = -2$.

3. $f(f(-3))$

• First, find $f(-3)$ from the graph of $f(x)$. From the graph, when $x = -3$, $f(-3) = -2$.
• Now, find $f(-2)$ from the graph of $f(x)$. From the graph, when $x = -2$, $f(-2) = 0$.
• Therefore, $f(f(-3)) = f(-2) = 0$.

4. $g(g(1))$

• First, find $g(1)$ from the graph of $g(x)$. From the graph, when $x = 1$, $g(1) = -1$.
• Now, find $g(-1)$ from the graph of $g(x)$. From the graph, when $x = -1$, $g(-1) = 1$.
• Therefore, $g(g(1)) = g(-1) = 1$.

Final Answers:

1. $f(g(-1)) = 5$
2. $g(f(0)) = -2$
3. $f(f(-3)) = 0$
4. $g(g(1)) = 1$

Would you like any further clarifications or detailed explanations on any of these steps?

Here are 5 related questions:

1. How do we interpret composite functions on graphs?
2. What is the significance of input-output mapping in function graphs?
3. How can you confirm your results when using multiple graphs?
4. What are common mistakes when reading values from function graphs?
5. How can you apply composite functions in real-world scenarios?

Tip: When reading graphs, always ensure you align the input values carefully on the x-axis to avoid errors in function evaluations.