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The task requires graphing the function \( g(x) = f(x) + 3 \) based on the provided graph of \( f(x) \), which is shown in red on the coordinate grid. Let's break down how to achieve this:

1. **Understanding the Transformation:** The function \( g(x) = f(x) + 3 \) represents a vertical translation of the graph of \( f(x) \). Specifically, every point on the graph of \( f(x) \) will be shifted upward by 3 units.

2. **Graphing \( g(x) \):**
   - Locate each point on the graph of \( f(x) \). Let's call these points \( (x_1, y_1) \).
   - For each point \( (x_1, y_1) \), the corresponding point on the graph of \( g(x) \) will be \( (x_1, y_1 + 3) \).
   - Move each point of the graph of \( f(x) \) vertically upward by 3 units and plot the new points.
   - Connect these new points to create the graph of \( g(x) \).

3. **Visualizing the Graph:** 
   - For the provided red graph, identify the key points where the lines change direction.
   - Shift these key points up by 3 units.
   - Redraw the lines maintaining the same shape as the original graph but shifted upward.

Would you like more details on this transformation process or how the new graph would look?

### 5 Relative Questions:
1. What would be the effect of the transformation \( g(x) = f(x) - 2 \)?
2. How would you graph \( g(x) = 2f(x) \) based on the original graph of \( f(x) \)?
3. What happens if the transformation is \( g(x) = f(x - 3) \) instead?
4. How do horizontal translations differ from vertical translations?
5. Can you describe how to reflect the graph of \( f(x) \) across the x-axis?

### Tip:
When applying transformations, always remember that changes outside the function \( f(x) \) (e.g., \( f(x) + k \)) affect the vertical movement, while changes inside the function (e.g., \( f(x - h) \)) affect the horizontal movement.

The graph of f(x) is shown in red. Draw the graph of g(x) = f(x) + 3. Make sure to start at one of the endpoints, not the middle point.

Learn how to graph the vertical shift of a function using g(x) = f(x) + 3. This problem covers function transformations and vertical shifts, with detailed graphing techniques. Suitable for students in Grades 8-10.

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