The graph of g and the graph of f are shown.

Two parallel lines graphed on a coordinate plane. Function F crosses the Y axis at four and function G crosses the Y axis at one.

Which of the following describes a single transformation that compares the graph of g with the graph of f? Select all that apply.
	A.	The graph of g is the graph of f shifted 3 units left.
	B.	The graph of g is the graph of f shifted 3 units right.
	C.	The graph of g is the graph of f shifted 3 units up.
	D.	The graph of g is the graph of f shifted 3 units down.
	E.	The graph of g is the graph of f scaled by a factor of 14
	F.	The graph of g is the graph of f scaled by a factor of 4.

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.

Two parallel lines are graphed on a coordinate plane. Function F crosses the Y axis at four, and function G crosses the Y axis at one. Which of the following describes a single transformation that compares the graph of g with the graph of f? Select all that apply. A. The graph of g is the graph of f shifted 3 units left. B. The graph of g is the graph of f shifted 3 units right. C. The graph of g is the graph of f shifted 3 units up. D. The graph of g is the graph of f shifted 3 units down. E. The graph of g is the graph of f scaled by a factor of 14. F. The graph of g is the graph of f scaled by a factor of 4.

This problem explains how to compare the graphs of two parallel lines with different y-intercepts. Learn how to identify vertical shifts and transformations in linear functions through this step-by-step solution. Suitable for students in Grades 8-10.

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