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The problem asks to "Draw the graph of \( y = 2h(x - 4) \)", based on a given graph of \( y = h(x) \). Since I can't see the actual graph of \( h(x) \), I can guide you through the transformation process.

To graph \( y = 2h(x - 4) \), follow these steps:

### 1. **Horizontal Shift** (due to \( x - 4 \)):
   - The expression \( x - 4 \) indicates a **horizontal shift**. Specifically, the graph of \( h(x) \) is shifted **4 units to the right**. So, every point \( (x, y) \) on the graph of \( h(x) \) will move to \( (x+4, y) \).

### 2. **Vertical Stretch** (due to the coefficient 2):
   - The factor of 2 outside the function indicates a **vertical stretch**. This means that the graph will be stretched by a factor of 2. In other words, if a point on the original graph of \( h(x) \) is at \( (x, y) \), it will now be at \( (x, 2y) \).

### 3. **Apply both transformations**:
   - First shift the graph horizontally by 4 units to the right.
   - Then, stretch it vertically by multiplying all the \( y \)-coordinates by 2.

If you have the graph of \( h(x) \) available, you can apply these transformations directly.

### Do you have any questions or would you like more detailed steps? 

Here are five questions to expand the concept:
1. How does the transformation \( y = h(x - c) \) generally affect the graph?
2. What happens if the function had been \( y = h(x + 4) \) instead?
3. How would a negative coefficient, like \( y = -2h(x - 4) \), affect the graph?
4. How do you interpret transformations that include both vertical and horizontal shifts?
5. Can the transformations \( y = 2h(x - 4) \) be applied in a different order (e.g., vertical stretch first)?

**Tip:** When applying transformations, always handle horizontal shifts inside the function (involving \( x \)) and vertical changes (like stretching or reflecting) outside the function.

The graph of y = h(x) is shown. Draw the graph of y = 2h(x - 4).

Learn how to apply graph transformations to the function y = 2h(x - 4). This problem covers horizontal shifts and vertical scaling, helping students understand key concepts in algebra and graph theory. Suitable for students in Grades 10-12.

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