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The problem asks, "Which input value produces the same output value for the two functions on the graph?"

The graph shows two linear functions, \( f(x) \) (red line) and \( g(x) \) (blue line). To answer the question, we need to find the \( x \)-value where both functions intersect, as this is where they produce the same output value.

By looking at the intersection of the two lines, the coordinates of the intersection appear to be at \( x = 1 \), where both functions seem to have the same output value of \( y = 2 \).

Thus, the correct input value is:

**\( x = 1 \)**

Would you like more details or explanations about how this solution was reached?

Here are 5 related questions to explore further:
1. What are the equations of the lines for \( f(x) \) and \( g(x) \)?
2. How do you find the intersection point of two linear functions algebraically?
3. What is the slope of each line based on the graph?
4. How does solving a system of equations graphically compare to solving it algebraically?
5. What does the point of intersection represent in real-world problems?

**Tip:** When two lines intersect on a graph, the \( x \)-coordinate at the intersection is where both functions produce the same output value (i.e., their \( y \)-values are equal).

Which input value produces the same output value for the two functions on the graph?

Learn how to find the intersection point of two linear functions by analyzing the graph. This problem demonstrates how to identify the input value where two functions produce the same output, focusing on concepts of linear equations and coordinate geometry. Ideal for Grades 8-10.

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