To solve $(f \circ g)(-7)$, we need to evaluate the composite function step by step using the graphs of $f(x)$ and $g(x)$.

Step 1: Evaluate $g(-7)$

Using the graph of the red line (which represents $g(x)$), we need to find the value of $g(-7)$. From the graph, when $x = -7$, the value of $g(x)$ is approximately 3 (because the red line passes through $(-7, 3)$).

Step 2: Evaluate $f(g(-7)) = f(3)$

Next, we use the graph of the blue line (which represents $f(x)$) to find the value of $f(3)$. From the graph, when $x = 3$, the value of $f(x)$ is approximately 6 (since the blue line passes through $(3, 6)$).

Conclusion:

Thus, $(f \circ g)(-7) = f(g(-7)) = f(3) = 6$.

The answer is $6$.

Would you like more details or have any questions?

Here are some related questions to consider:

1. What is the difference between a composite function and a regular function?
2. Can a composite function have more than two functions?
3. How do we know which graph represents $f(x)$ and which represents $g(x)$?
4. What are other methods to evaluate composite functions if graphs are not available?
5. How can we interpret composite functions in real-world applications?

Tip: Always check the axis labels and values carefully on graphs to avoid misreading the function outputs.