https://file.aiquickdraw.com/mathbot/file/17261898501423g5ykz93.jpg

The question asks to approximate the value of \( (f \circ g)(-2) \), which represents the composition of the functions \( f(x) \) and \( g(x) \) evaluated at \( x = -2 \).

To find this, we need to follow these steps:
1. First, find \( g(-2) \) by evaluating \( g(x) \) at \( x = -2 \).
2. Then, take the result of \( g(-2) \) and use it as the input for \( f(x) \), i.e., calculate \( f(g(-2)) \).

### Step 1: Evaluate \( g(-2) \)
Looking at the graph, the purple curve represents \( g(x) \). At \( x = -2 \), the graph of \( g(x) \) intersects the y-axis at approximately \( y = 2 \). Thus, \( g(-2) \approx 2 \).

### Step 2: Evaluate \( f(g(-2)) = f(2) \)
Now, use \( g(-2) = 2 \) as the input for \( f(x) \), which is represented by the blue curve. From the graph, when \( x = 2 \), the graph of \( f(x) \) intersects the y-axis at approximately \( y = 1 \). Therefore, \( f(2) \approx 1 \).

### Final Answer:
Thus, \( (f \circ g)(-2) \approx 1 \).

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Would you like more details on any of the steps? Here are five related questions to deepen understanding:

1. What does the composition of functions mean mathematically?
2. How would you describe the relationship between \( f(x) \) and \( g(x) \) graphically?
3. What happens if we reverse the composition, i.e., \( (g \circ f)(-2) \)?
4. How does the shape of the function graph affect its values at given points?
5. Can you provide an example where \( f \circ g \) results in a negative value?

**Tip:** When interpreting a graph, it's essential to estimate values carefully by observing where the curve intersects the grid lines.

¿Cuál de las siguientes aproxima mejor el valor de (f ◦ g)(-2)?

Learn how to approximate the value of the composition of two functions, f(x) and g(x), at x = -2 using graphical interpretation. Suitable for students in Grades 9-11.

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