Let's analyze the three functions $f(x)$, $g(x)$, and $h(x)$ based on their graphs. Afterward, we'll solve the two given expressions $f(g(2))$ and $g(h(-3))$.

1. Solving $f(g(2))$:

• First, we need to determine $g(2)$ from the graph of $g(x)$. From the graph, $g(2) = 1$.
• Now, substitute $g(2) = 1$ into $f(x)$. From the graph of $f(x)$, we see that $f(1) = 1$.

Thus, $f(g(2)) = 1$.

2. Solving $g(h(-3))$:

• First, we find $h(-3)$ from the graph of $h(x)$. From the graph, $h(-3) \approx -1$.
• Next, substitute $h(-3) = -1$ into $g(x)$. From the graph of $g(x)$, we see that $g(-1) = 0$.

Thus, $g(h(-3)) = 0$.

Answers:

• $f(g(2)) = 1$
• $g(h(-3)) = 0$

Would you like more details, or do you have any questions about this? Here are some related questions to expand on this topic:

1. How do you find the value of a composite function from its graph?
2. Can we generalize the process of finding composite functions without graphs?
3. How do we determine the domain and range of a composite function?
4. What happens to the composite function if one of the functions is not defined at a specific point?
5. How does the order of function composition affect the result?

Tip: When working with composite functions, always resolve the innermost function first before proceeding to the outer function.