To analyze the transformations from \( f(x) = x \) to \( f(3x) - \frac{1}{3} = 3x - \frac{1}{3} \), let's break down the transformations step by step:
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Start with \( f(x) = x \).
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Transform to \( f(3x) \):
- This represents a horizontal compression by a factor of 3. The function \( f(3x) \) compresses the graph horizontally because the input values are scaled by a factor of \( \frac{1}{3} \).
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Then apply \( -\frac{1}{3} \):
- After obtaining \( f(3x) = 3x \), we then have \( f(3x) - \frac{1}{3} \). This operation shifts the entire graph down by \( \frac{1}{3} \).
Combining these transformations, we find that the correct identification is:
Compressed horizontally and shifted down.
So the correct choice is:
- compressed horizontally and shifted down.