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The question asks which input value produces the same output value for the two functions \( f(x) \) and \( g(x) \) shown on the graph. We need to find the point where both functions intersect, as that would represent the input where the output values for both functions are equal.

### Analysis of the Graph:

- The red line represents \( f(x) \), which appears to be a constant function at \( y = 3 \) (a horizontal line).
- The blue line represents \( g(x) \), which is a line with a positive slope.

We are asked to determine where these two lines have the same output value, which occurs at the point of intersection.

By observing the graph:
- The two lines intersect at \( x = 3 \) with a common \( y \)-value of 3.

### Conclusion:
The correct input value where the two functions have the same output is \( x = 3 \).

Would you like further details on the solution?

Here are 5 related questions:
1. What is the general form of the equation for a line with a positive slope?
2. How do you determine the slope of a line from a graph?
3. What are the key characteristics of a constant function?
4. How can you algebraically find the intersection point of two functions?
5. What is the meaning of an "output value" in a function?

**Tip:** Always check for the intersection point between two graphs to find where their outputs are equal.

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

Explore how to determine the intersection point of two linear functions graphically. This tutorial includes step-by-step graphical analysis, suitable for students in grades 8-10, covering key concepts such as the equation of a line and methods to find intersection points.

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