To evaluate $g(f(-7))$, we need to follow these steps:

1. Find $f(-7)$ from the graph of $f(x)$ (on the left).
2. Use the value of $f(-7)$ to find $g(f(-7)) = g(\text{value})$ using the graph of $g(x)$ (on the right).

Step 1: Find $f(-7)$

• From the graph of $f(x)$ on the left, locate $x = -7$.
• The corresponding $y$-value at $x = -7$ is $f(-7) = 9$.

Step 2: Find $g(f(-7)) = g(9)$

• Now, go to the graph of $g(x)$ (on the right) and locate $x = 9$.
• The corresponding $y$-value at $x = 9$ is $g(9) = 7$.

Final Answer:

Therefore, $g(f(-7)) = 7$.

Would you like further details or explanations on any part of the process?

Here are 5 related questions to expand your understanding:

1. What does it mean when we perform a composition of functions like $g(f(x))$?
2. How do you determine the range of $f(x)$ and $g(x)$ from their graphs?
3. What are other ways to solve composite functions besides using graphs?
4. How can you determine whether $f(x)$ or $g(x)$ is one-to-one or onto by observing the graph?
5. How does the behavior of the graphs affect the values of composite functions?

Tip: When working with composite functions, always evaluate the inner function first before moving on to the outer function.