The problem asks to find $(f \circ g)(-5)$, which is the composition of the functions $f(x)$ and $g(x)$, evaluated at $-5$.

Steps:

1. Understand the composition: $(f \circ g)(x) = f(g(x))$. We need to first evaluate $g(-5)$, then use that result to find $f(g(-5))$.

2. Find $g(-5)$: From the graph, the black curve represents $g(x)$. At $x = -5$, follow the curve to the y-value.

   • Looking at the graph, the black curve passes through $(-5, 4)$, so $g(-5) = 4$.

3. Find $f(g(-5)) = f(4)$: Now, use the blue curve (representing $f(x)$) to find $f(4)$.

   • From the graph, the blue curve passes through $(4, -4)$, so $f(4) = -4$.

Thus, $(f \circ g)(-5) = f(g(-5)) = f(4) = -4$.

Final Answer:

$(f \circ g)(-5) = -4$

Would you like more details or have any questions? Here are five related questions to consider:

1. How do you determine $g(x)$ and $f(x)$ values from a graph?
2. What are the properties of function composition?
3. Can you explain how to graphically interpret $(f \circ g)(x)$?
4. How does the domain of a composite function differ from individual functions?
5. What happens if a graph is not continuous—how does that affect composition?

Tip: Always follow the correct order when solving function compositions: evaluate the inner function first before applying the outer function.