To find the values for \( y = f(-x) \) based on the graph of \( y = f(x) \), we need to reflect the values of \( f(x) \) across the y-axis.
This means that for every \( x \) value in the function \( f(x) \), we retrieve the corresponding \( y \) value from \( f(x) \), but for \( -x \), we take the \( y \) value from \( f(x) \) at \( x \).
Let's say we have found the values \( f(x) \) for specific \( x \):
- For \( x = 1 \), \( f(1) = y_1 \)
- For \( x = 2 \), \( f(2) = y_2 \)
- For \( x = 3 \), \( f(3) = y_3 \)
To find \( f(-x) \):
- For \( -1 \), \( f(-1) = f(1) \)
- For \( -2 \), \( f(-2) = f(2) \)
- For \( -3 \), \( f(-3) = f(3) \)
Now we can map out potential responses based on the values of \( f(x) \).
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Inspect the first option:
- \( f(-1) = 2 \)
- \( f(-2) = 0 \)
- \( f(-3) = 2 \)
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For the second option:
- \( f(-1) = 2 \)
- \( f(-2) = 0 \)
- \( f(-3) = 2 \)
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For the third option:
- For negatives, these seem incorrect.
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Last option (checking):
- \( f(-1) = -2 \)
- \( f(-2) = 0 \)
- \( f(-3) = -2 \)
Based on the reflection rule, the values derived should correspond to those seen at their positive \( x \) partners.
Given our context in analysis, the values that appear valid from the likely direct reflection from f(x) aligns with:
- First choice containing outputs \( 2, 0, 2 \) for respective inputs at \( -1, -2, -3 \).
So we'll select this correctly reflected table correspondingly that matches the transformation of negative values to original points in function by extrapolating from positive ones.
The best response would be:
x f(−x) -1 2 -2 0 -3 2