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The problem is asking you to graph the function \( g(x) = f(x) + 3 \) based on the given graph of \( y = f(x) \).

### Key Concept:
The transformation \( g(x) = f(x) + 3 \) represents a **vertical shift** of the function \( f(x) \) upwards by 3 units. This means that each point on the graph of \( f(x) \) will be moved 3 units higher on the \( y \)-axis.

### Procedure:
1. Identify key points on the graph of \( f(x) \). For example, look at the points where the graph changes direction or passes through the axes.
2. Shift each of these points 3 units upwards. That means, for any point \( (x, y) \) on \( f(x) \), the corresponding point on \( g(x) \) will be \( (x, y+3) \).
3. The new graph should maintain the same shape as the original, but just shifted vertically.

### Comparison with the Options:
From the given options:
- **Option A** shows a graph shifted downwards, which would correspond to a subtraction transformation, not an addition.
- **Option B** shows the graph at the same vertical level, meaning no vertical shift, which is incorrect.
- **Option C** shows the graph shifted correctly upwards by 3 units, maintaining the shape of the original graph.
- **Option D** shows an incorrect vertical shift.

Thus, the correct answer is **Option C**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the graph change if the transformation were \( g(x) = f(x) - 2 \)?
2. What is the effect of the transformation \( g(x) = 2f(x) \) on the graph?
3. How do horizontal shifts differ from vertical shifts in graph transformations?
4. Can you describe the transformation represented by \( g(x) = f(x - 2) \)?
5. How would the graph of \( f(x) \) change under a reflection over the x-axis?

**Tip**: Vertical shifts only affect the \( y \)-values of the points, not the \( x \)-values.

Use the graph of y = f(x) to graph the function g(x) = f(x) + 3. Choose the correct graph of g from the options.

Learn how to graph the function g(x) = f(x) + 3 by applying vertical shifts. This problem explores graph transformations and is suitable for students in Grades 8-10. Practice identifying correct graphs based on function shifts.

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