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The question asks you to use the graph of the function \( f \), plotted with a solid line, and sketch the graph of \( g(x) = f(x+2) - 2 \).

Let's break down what \( g(x) = f(x+2) - 2 \) means in terms of transformations of the graph of \( f(x) \):

1. **\( f(x+2) \)**: This represents a horizontal shift. The graph shifts **2 units to the left** (because adding inside the function causes a shift in the opposite direction).
2. **\( -2 \)**: This represents a vertical shift. The graph shifts **2 units downward**.

So, to obtain the graph of \( g(x) \) from the graph of \( f(x) \), we shift the graph of \( f(x) \) **2 units to the left** and **2 units downward**.

### Now, let's analyze the options:
- **Option A**: This shows a graph shifted **2 units to the right**, which is incorrect.
- **Option B**: This shows a graph shifted **2 units to the left**, but no vertical shift.
- **Option C**: This graph is **shifted 2 units to the left and 2 units downward**, which is correct.
- **Option D**: This shows a graph shifted **downward** but without the horizontal shift.

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

Would you like more details on transformations or have any further questions?

### Here are 5 related questions to explore further:
1. What happens if the function \( g(x) \) is \( f(x-3) + 4 \)?
2. How would the transformation change if the equation was \( g(x) = 2f(x) \)?
3. What are the effects of a vertical stretch on a graph?
4. Can you explain how a reflection across the x-axis affects the graph of \( f(x) \)?
5. How do you find the vertex of a transformed quadratic function?

### Tip: 
For any transformation, changes inside the function (like \( x+2 \)) affect the graph horizontally, and changes outside the function (like \( -2 \)) affect it vertically.

Use the graph of the function f, plotted with a solid line, to sketch the graph of g(x) = f(x + 2) - 2.

Learn how to perform graph transformations by shifting the function g(x) = f(x + 2) - 2. This covers horizontal and vertical shifts, key concepts in algebra and graphing for students in Grades 9-12.

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