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

The transformation \( g(x) = f(x + 2) \) represents a **horizontal shift**. In this case, the graph of \( f(x) \) is shifted **to the left by 2 units** because the \( +2 \) inside the function affects the \( x \)-values, shifting the graph leftward.

Looking at the original graph of \( f \), which appears to be a parabola opening upward, the correct transformation would shift this parabola two units to the left.

Now, let's check the options:

- **Option A**: This graph is shifted **right**, so it is incorrect.
- **Option B**: This graph seems to be a **leftward shift** by 2 units, which looks correct.
- **Option C**: This graph also appears to be a **leftward shift**, but it is **shifted too far**.
- **Option D**: This graph is shifted **right**, which is incorrect.

So, the correct choice is **Option B**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the effect of \( g(x) = f(x - c) \) on the graph of \( f(x) \)?
2. How does a vertical shift differ from a horizontal shift in graph transformations?
3. What happens if the transformation is \( g(x) = f(x - 2) \) instead?
4. Can you explain how transformations affect the vertex of a parabola?
5. How do you determine the direction of a shift based on the equation?

**Tip:** Remember that shifts inside the parentheses affect the graph horizontally, while those outside 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).

Learn how to shift the graph of f(x) to the left by 2 units using the transformation g(x) = f(x + 2). This problem focuses on function transformations and is ideal for students in Grades 8-10.

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