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The question describes two functions: \( f(x) = x \) and \( g(x) = f(x) - 3 = x - 3 \). It asks how the graphs of \( f \) and \( g \) are related.

- The graph of \( f(x) = x \) is a straight line passing through the origin with a slope of 1.
- The function \( g(x) = x - 3 \) is simply a vertical shift of \( f(x) \) by 3 units downward (since subtracting a constant moves the graph down).

Thus, the correct answer is **C: The graph of \( f \) is shifted 3 units down to create the graph of \( g \)**.

Would you like more details on how shifts work for functions?

Here are 5 related questions for further practice:

1. What happens to the graph of \( f(x) \) if we add a constant, say 5, to it (i.e., \( f(x) = x + 5 \))?
2. How does multiplying the function \( f(x) = x \) by a constant affect the graph?
3. What is the effect of subtracting a constant from the \( x \)-coordinate instead of from the \( y \)-coordinate (e.g., \( f(x - 3) \))?
4. How would the graph change if we used \( g(x) = -f(x) \) instead?
5. What are the effects of combining both vertical and horizontal shifts in a graph?

**Tip:** Always remember that adding or subtracting a constant from a function shifts the graph vertically!

A student graphed f(x) = x and g(x) = f(x) - 3 on the same coordinate grid. Which statement describes how the graphs of f and g are related?

Learn how the graph of f(x) = x is related to the graph of g(x) = f(x) - 3 through vertical shifts. This problem explores key concepts in linear functions and graph transformations, making it suitable for students in Grades 8-10.

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