To find the values of \( y = f(-x) \) based on the original graph of \( y = f(x) \), we need to reflect the points of the graph across the y-axis. This means that for every \( x \) value, we will take the corresponding \( f(x) \) value and switch the sign of \( x \), effectively finding \( f(-x) \).
Without the actual image of the graph, I must describe the general approach:
- Identify key points on the graph of \( y = f(x) \).
- For each point \( (x, y) \) on that graph, find the point \( (-x, y) \) for the graph of \( y = f(-x) \).
- Organize these points into a table format.
Given the options you've provided, we would need to match the reflected points to the given tables.
Here’s a breakdown of the provided tables, looking for potential reflections:
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First table:
- \( x: -1 \rightarrow 2 \)
- The \( y \) value is different; continue checking.
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Second table:
- \( x: 1 \rightarrow -2 \)
- Matches if the original \( f(1) = -2 \).
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Third table:
- \( x: -1 \rightarrow 2 \) (there’s a non-matching \( y \) here as well).
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Fourth table:
- \( x: 1 \rightarrow 2 \)
- Again, it seems to ignore the negative reflection.
To choose the table that represents \( y = f(-x) \), look at the combinations of \( (x, f(-x)) \) ensuring to reflect each point accurately from \( y = f(x) \) to \( f(-x) \).
If matching the reflected values of the original graph supports the second table, where all points reflect correctly, that would be the right choice.
Without the actual graph, I suggest evaluating the points one by one with the reflection principle above to finalize your choice. If you can share the actual graph being referenced, I could give a more specific response based on identified transformations.
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