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The problem asks you to draw the graph of \( y = 2g(x) + 4 \) based on the given graph of \( y = g(x) \).

To help you adjust the graph correctly, here’s how to modify \( g(x) \):

1. **Vertical Stretch by a Factor of 2**: 
   - Since the equation includes \( 2g(x) \), the graph of \( g(x) \) will be stretched vertically by a factor of 2. This means that all points on the graph will be twice as far from the x-axis. For example, if \( g(x) = 1 \), then \( 2g(x) = 2 \); if \( g(x) = -2 \), then \( 2g(x) = -4 \).

2. **Vertical Shift by 4 Units Up**:
   - The "+4" in the equation shifts the graph 4 units upward. So, after applying the vertical stretch, you'll move all points up by 4 units.

### Steps to draw \( y = 2g(x) + 4 \):
- First, take each point on the graph of \( g(x) \) and multiply the y-coordinate by 2.
- Then, shift each resulting point up by 4 units on the y-axis.

Would you like more details or have any questions? Here are five related questions that might help you:

1. How does a vertical stretch change the graph's appearance compared to a vertical compression?
2. What would happen if the function had a negative sign in front of \( g(x) \), like \( -g(x) \)?
3. How does shifting a graph horizontally differ from shifting it vertically?
4. Can you explain how to combine multiple transformations like scaling and shifting on a graph?
5. What happens if both the x- and y-coordinates are transformed simultaneously?

**Tip:** Always apply stretching or shrinking transformations before shifting when working with function graphs.

The graph of y = g(x) is shown. Draw the graph of y = 2g(x) + 4.

Learn how to draw the graph of y = 2g(x) + 4 by applying vertical stretch and shift to the graph of y = g(x). This step-by-step solution explains the transformation process, including a vertical stretch by a factor of 2 and a vertical shift 4 units upward. Suitable for students in Grades 9-11.

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