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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.

Use the graphs of f and g to evaluate the composite function (f o g)(-7).

Learn how to evaluate the composite function (f o g)(-7) using the provided graphs of f(x) and g(x). This problem focuses on function evaluation and graph interpretation. Ideal for Grades 9-11 math students.

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