In this case, we are working with the transformation of the function $f(x) = x$ to $g(x) = 3f(x)$, which becomes $g(x) = 3x$.

Understanding the transformations:

• $f(x) = x$ is the equation of a straight line with a slope of 1, passing through the origin (0, 0).
• $g(x) = 3x$ is also a straight line passing through the origin, but with a slope of 3, meaning it is steeper than $f(x)$.

Key points to look for in the graphs:

1. Graph of $f(x) = x$:

   • A diagonal line with slope 1, passing through points like (0, 0), (1, 1), and (-1, -1).

2. Graph of $g(x) = 3x$:

   • A steeper diagonal line with slope 3, passing through points like (0, 0), (1, 3), and (-1, -3).

Now, let’s examine the possible graphs based on these details:

• Graph A: Compare the lines, checking which one is steeper (if any).
• Graph B: Check if there is a clear difference between the slope of $f(x)$ and $g(x)$.
• Graph C: Look for a graph where one line has a slope of 1, and the other has a slope of 3.
• Graph D: Check for similar features.

Once you've checked these details, choose the graph where:

• One line has a slope of 1 (for $f(x)$).
• The other line has a slope of 3 (for $g(x)$).

If you provide the graphs, I can help you identify which one correctly represents the transformation!

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Do you want more detailed information on identifying graph transformations?

Here are 5 related questions to deepen your understanding:

1. What happens when you multiply a function by a constant factor?
2. How does the slope of a line change with different transformations?
3. What are vertical stretches in function transformations?
4. How would a graph of $g(x) = -3x$ differ from $f(x) = x$?
5. What does shifting a graph horizontally or vertically look like?

Tip: A larger coefficient in front of $x$ makes the graph steeper, while a smaller coefficient flattens it.