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The problem now involves the function transformation \( g(x) = 3f(x) \).

This transformation involves a **vertical stretch** by a factor of 3. Specifically, every y-coordinate of the original graph of \( f(x) \) will be multiplied by 3. This means that each point on the graph will be stretched away from the x-axis by a factor of 3, while the x-coordinates remain unchanged.

### Step-by-step process:
1. For each point on the original graph of \( f(x) \), multiply the y-coordinate by 3.
   - For example, if a point on \( f(x) \) is \( (x, y) \), the corresponding point on \( g(x) \) will be \( (x, 3y) \).
2. Leave the x-coordinates the same.
3. Sketch the new graph after applying this vertical stretch.

### Now, let's analyze the options:
- **Option A:** This graph shows the correct vertical stretch, where the y-values have been multiplied by 3, causing the graph to stretch away from the x-axis.
- **Options B, C, and D** do not reflect the correct vertical scaling; they either appear compressed or have incorrect points.

Thus, **Option A** is the correct graph.

Let me know if you'd like more detailed information or have any questions!

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Here are 5 related questions for further exploration:
1. What happens to the graph if the function is \( g(x) = \frac{1}{2}f(x) \)?
2. How does a negative vertical stretch, such as \( g(x) = -3f(x) \), affect the graph?
3. What is the general effect of multiplying a function by a constant on the graph?
4. Can you explain the difference between vertical and horizontal stretches?
5. How would you graph \( g(x) = 2f(x) + 3 \), which involves both a vertical stretch and a vertical shift?

**Tip:** A vertical stretch \( g(x) = a \cdot f(x) \) stretches or compresses the graph by a factor of \( a \) in the y-direction. If \( |a| > 1 \), the graph stretches; if \( 0 < |a| < 1 \), it compresses.

Use the graph of y = f(x) shown below to graph the function g, where g(x) = 3f(x). Choose the correct graph below from the options provided.

Explore how to transform the graph of y = f(x) using the function g(x) = 3f(x). This problem demonstrates a vertical stretch transformation, where every y-coordinate is multiplied by 3. Suitable for high school students in Grades 9-12.

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