To solve $f(h(1))$, we need to follow these steps:

1. Evaluate $h(1)$ using the graph of $h(x)$ shown in Figure 2.

   • Locate $x = 1$ on the $h(x)$ graph.
   • From the graph, when $x = 1$, the value of $h(x)$ is $h(1) = -2$.

2. Evaluate $f(-2)$ using the graph of $f(x)$ shown in Figure 1.

   • Now, locate $x = -2$ on the $f(x)$ graph.
   • From the graph, when $x = -2$, the value of $f(x)$ is $f(-2) = 4$.

Thus, the answer is: $f(h(1)) = f(-2) = 4$

Would you like further explanation or have any questions?

Here are five related questions to expand on this topic:

1. How do you evaluate nested functions when both functions are linear?
2. What happens if $f(x)$ or $h(x)$ includes more than one solution for a given input?
3. How would the solution change if we used a different input for $h(x)$ in this example?
4. What is the process for finding $h(f(1))$ instead of $f(h(1))$?
5. How can you determine if the functions are one-to-one based on their graphs?

Tip: Always double-check each function’s output before plugging it into the next function in a composition.