https://file.aiquickdraw.com/mathbot/file/1727016698813g5iknosg.jpg

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 \( 6 \).

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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.

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

Learn how to solve a composite function using graphs. This problem covers key mathematical concepts like function composition and graph interpretation, suitable for students in Grades 8-10.

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