https://file.aiquickdraw.com/mathbot/file/17261962248747j6arugg.jpg

The problem asks to use the graph of \( y = f(x) \) to graph the function \( g(x) = f(x + 2) \). 

The transformation \( g(x) = f(x + 2) \) is a horizontal shift of the graph of \( f(x) \) to the left by 2 units. In other words, every point on the graph of \( f(x) \) will be shifted 2 units to the left to create the graph of \( g(x) \).

### Step-by-step process:
1. Take each point on the original graph of \( f(x) \).
2. Move each point 2 units to the left.
3. Sketch the new graph after this transformation.

Now let's analyze the options:

- **Option A:** This graph shows a horizontal shift to the **left** by 2 units, which matches the transformation \( f(x + 2) \).
- **Options B, C, and D** do not show the correct horizontal shift to the left by 2 units.

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 relative questions for further exploration:
1. What happens to the graph when \( g(x) = f(x - 2) \)?
2. How do vertical shifts affect the graph of a function?
3. Can you explain the effect of a reflection, such as \( g(x) = -f(x) \)?
4. What is the general rule for shifting functions horizontally?
5. How does a combination of transformations (like shifts and reflections) affect the graph of a function?

**Tip:** Remember that a transformation of \( g(x) = f(x + h) \) shifts the graph **left** if \( h > 0 \), and **right** if \( h < 0 \).

Use the graph of y = f(x) to graph the function g(x) = f(x + 2).

Learn how to use graph transformations to graph the function g(x) = f(x + 2) by shifting the original function f(x) to the left by 2 units. Understand key mathematical concepts of function transformations, including horizontal shifts. Suitable for students in Grades 9-11.

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