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The problem asks for the correct table representation of the function \( y = f(-x) \) based on the graph of the original function \( y = f(x) \).

### Key concept:
When you substitute \( -x \) into the function, you reflect the graph of \( f(x) \) across the y-axis. This means that the output values will remain the same, but the input values (x-values) will change signs. Specifically:
- If \( f(a) = b \), then \( f(-a) = f(a) = b \).

### To analyze the tables:
We look for the table where the x-values have been reflected, but the corresponding \( f(x) \) values are unchanged.

#### Steps:
- If \( f(x) = -2 \) when \( x = 1 \), then \( f(-1) = -2 \).
- If \( f(x) = 0 \) when \( x = 2 \), then \( f(-2) = 0 \).
- If \( f(x) = -2 \) when \( x = 3 \), then \( f(-3) = -2 \).

Looking at the four options, the correct table is the third one:
\[
\begin{array}{|c|c|}
x & f(-x) \\
\hline
-1 & -2 \\
-2 & 0 \\
-3 & -2 \\
\end{array}
\]
This correctly reflects the x-values and keeps the \( f(x) \) values the same.

### Answer: 
The third table is the correct representation of \( y = f(-x) \).

Would you like more details, or do you have any further questions?

Here are 5 follow-up questions related to this concept:
1. What happens to the graph of a function when you reflect it over the y-axis?
2. Can you find a function that remains the same after reflecting over the y-axis?
3. How do you reflect a graph over the x-axis, and what would that look like in a table?
4. What is the effect on the graph if you reflect both over the x- and y-axes?
5. How would the table look if the transformation were \( y = -f(-x) \)?

**Tip:** When transforming functions, pay attention to whether the change is applied to the x-values or y-values, as this determines whether the transformation affects the horizontal or vertical positioning.

The original graph of the function y = f(x) is shown. Select the table that represents y = f(-x).

Learn how to identify the correct table representation of y = f(-x), reflecting a function across the y-axis. This problem involves understanding function transformations, particularly graph reflections. Suitable for students in Grades 9-11.

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