To solve the composite function $(f \circ g)(-7)$, we will break down the steps using the graphs provided for $f(x)$ and $g(x)$.

Steps:

1. Evaluate $g(-7)$: From the graph of $g(x)$, which is the red line, find the value of $g(x)$ when $x = -7$. Locate $x = -7$ on the horizontal axis, trace upwards or downwards to find the red point. Based on the graph: $g(-7) = 1$

2. Evaluate $f(g(-7)) = f(1)$: Now, using the value $g(-7) = 1$, evaluate $f(1)$. From the graph of $f(x)$, which is the blue line, locate $x = 1$ on the horizontal axis, and trace upwards to find the blue point. Based on the graph: $f(1) = 7$

Final Answer:

$(f \circ g)(-7) = f(g(-7)) = f(1) = 7$

Would you like further details or have any questions about this solution?

Here are 5 related questions:

1. What is the general definition of a composite function?
2. How can you determine if a composite function is defined for all values of $x$?
3. Can you calculate $(g \circ f)(-7)$ using the same graph?
4. How do you evaluate a composite function algebraically without a graph?
5. What properties do the graphs of $f(x)$ and $g(x)$ exhibit (e.g., symmetry, slope)?

Tip: When working with composite functions, always evaluate the inner function first, then substitute its result into the outer function.