The key observation here is that the graphs of $f$ and $g$ are parallel lines, which means they have the same slope. The only difference between them is their vertical positions, as described by their y-intercepts.

• $f(x)$ crosses the y-axis at 4, so its y-intercept is 4.
• $g(x)$ crosses the y-axis at 1, so its y-intercept is 1.

Now, since both lines are parallel, no scaling has taken place. The only transformation involved is a vertical shift. To move the graph of $f(x)$ (which crosses at 4) to match the graph of $g(x)$ (which crosses at 1), you need to shift $f(x)$ down by 3 units.

Correct answer:

• D. The graph of $g$ is the graph of $f$ shifted 3 units down.

Incorrect options:

• A and B: No horizontal shifts are involved (the lines have the same slope and position on the x-axis).
• C: The shift is downward, not upward.
• E and F: The lines are not scaled, as they are parallel and retain the same slope.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:

1. How do you determine if two lines are parallel from their equations?
2. What transformations affect the slope of a line?
3. How can you identify vertical shifts from a function's equation?
4. What happens to the graph of a line if it is scaled vertically?
5. How does changing the y-intercept of a function affect its graph?

Tip: When comparing graphs, focus on shifts for changes in position and scaling for changes in steepness or stretching.