We are tasked with sketching the graph of $y = 3f(x)$ based on the points from the graph of $y = f(x)$. The transformation described, $y = 3f(x)$, is a vertical stretch by a factor of 3. This means every $y$-coordinate on the graph of $f(x)$ will be multiplied by 3, while the $x$-coordinates remain the same.

Step-by-step breakdown:

1. The point (-4,0):

   • Since the $y$-value is 0, multiplying it by 3 doesn't change its position.
   • Shifted point: (-4,0).

2. The point (-2,2):

   • Here, the $y$-value is 2. Applying the transformation, we multiply 2 by 3.
   • Shifted point: (-2, 6).

3. The point (0,0):

   • Similar to the first point, the $y$-value is 0, and multiplying by 3 will result in no change.
   • Shifted point: (0,0).

4. The point (2,2):

   • The $y$-value is 2, and multiplying it by 3 gives 6.
   • Shifted point: (2,6).

Now, based on these transformations, the correct sketch of the graph would have these vertical stretches applied to the relevant points. Looking at the choices:

• Option A appears to show no significant vertical stretching.
• Option B shows a graph with a stretched peak, matching the new values of $y$ after multiplying by 3.
• Option C and Option D do not seem to match the required scaling.

Thus, the best sketch for $y = 3f(x)$ is B.

Would you like to dive deeper into this? Here are 5 related questions to further explore:

1. How does a horizontal stretch or compression differ from a vertical stretch?
2. What transformation would result in a reflection over the x-axis?
3. How does adding a constant to $f(x)$ affect the graph?
4. Can you explain the effect of applying a vertical translation to $f(x)$?
5. How does the transformation $y = -f(x)$ affect the graph?

Tip: Always keep track of transformations by focusing on how they impact key points (like intercepts or turning points) on the graph!