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The graph shows a function \( y = f(x) \), and you are asked to draw the graph of \( y = 2f(x) \), which represents a vertical stretch of the original graph by a factor of 2.

### Explanation of the transformation:
When we multiply a function \( f(x) \) by 2, the result \( 2f(x) \) means that the \( y \)-coordinates of all points on the graph of \( f(x) \) will be doubled, while the \( x \)-coordinates remain unchanged. This transformation stretches the graph vertically.

Looking at the given graph of \( y = f(x) \), you can follow these steps to draw the new graph \( y = 2f(x) \):
1. **Identify key points on the original graph:** Look for easy-to-read points such as where the function crosses the grid lines.
2. **Apply the transformation:** Double the \( y \)-coordinates of these points while keeping the \( x \)-coordinates the same.
3. **Plot the transformed points:** Connect them to create the new graph.

For example:
- If there is a point on the original graph at \( (-2, -2) \), its transformed point for \( y = 2f(x) \) would be \( (-2, -4) \), since the \( y \)-value is doubled.

Would you like more details on how to plot the points, or any further clarification on the transformation? 

Here are 5 relative questions that could expand this topic:
1. What happens to the graph if you multiply by a factor less than 1, such as \( y = \frac{1}{2}f(x) \)?
2. How would the transformation change if it were applied horizontally instead of vertically (e.g., \( y = f(2x) \))?
3. How do you reflect a graph across the \( x \)-axis, and how does that compare to a vertical stretch?
4. What happens if the function \( y = -f(x) \) is used instead of \( y = f(x) \)?
5. How does a vertical translation (e.g., \( y = f(x) + 3 \)) differ from a vertical stretch?

**Tip:** When transforming graphs, always keep track of the impact on key points, such as intercepts and turning points, to visualize the changes clearly.

The graph of y = f(x) is shown. Draw the graph of y = 2f(x).

Understand how to apply vertical stretching to a graph using the transformation y = 2f(x). This problem demonstrates how the y-values of points on the graph are doubled while the x-values remain the same, changing the graph's shape.

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