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The problem you're looking at asks about two graphed functions, \( f(x) \) and \( g(x) \), which are plotted in blue and red, respectively. We need to determine which statement regarding these functions is true based on the graph.

Let's analyze the options step by step:

1. **\( f(4) = g(4) \)**: This means at \( x = 4 \), the values of both \( f(x) \) and \( g(x) \) must be equal. Looking at the graph:
   - The value of \( f(4) \) appears to be around \(-12\).
   - The value of \( g(4) \) appears to be around \(6\).
   Since these values are not equal, this option is **false**.

2. **\( f(-2) = g(-2) \)**: This means at \( x = -2 \), the values of both functions must be the same. 
   - The value of \( f(-2) \) appears to be about \(6\).
   - The value of \( g(-2) \) is also around \(6\).
   Since these values are equal, this statement is **true**.

3. **\( f(2) = g(-2) \)**: This compares \( f(2) \) and \( g(-2) \).
   - The value of \( f(2) \) seems to be around \( -6 \).
   - The value of \( g(-2) \) is \(6\), as noted earlier.
   These values are not equal, so this option is **false**.

4. **\( f(4) = g(-2) \)**: This compares \( f(4) \) and \( g(-2) \).
   - \( f(4) \) is around \(-12\).
   - \( g(-2) \) is \(6\).
   These values are not equal, so this option is **false**.

The correct answer is **\( f(-2) = g(-2) \)**, or the second option.

Would you like more details or have any questions? Here are some related questions:

1. How do you find the value of a function at a specific point from a graph?
2. How can we determine if two functions are equal at a particular \( x \)-value?
3. What are the key characteristics to observe in a graph to identify intersections?
4. How do linear functions differ in slope and y-intercept?
5. How can we use function notation effectively in evaluating graph-based problems?

**Tip:** Always check the points of intersection in a graph as they often provide answers where two functions are equal at specific values.

Which statement is true regarding the graphed functions?

Understand how to compare two functions using graph analysis. This problem involves determining points where two graphed functions are equal by analyzing their intersection points and specific values.

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