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!