Which of the following correctly identifies the transformations undergone from f(x)=x to f(3x)-1/3= 3x-1/3

To analyze the transformation from \( f(x) = x \) to \( f(3x) - \frac{1}{3} = 3x - \frac{1}{3} \), let's break it down step by step.

1. Starting function: \( f(x) = x \)

2. Transformation to \( f(3x) \):

   • Replacing \( x \) with \( 3x \) compresses the graph horizontally by a factor of 3. This means that for any value of \( y \), you need \( x \) to be a third of what it was in the original function to produce the same \( y \) value.

3. Transformation to \( f(3x) - \frac{1}{3} \):

   • The expression \( f(3x) - \frac{1}{3} \) indicates a vertical shift downward by \( \frac{1}{3} \).

Putting it all together:

• The transformation from \( f(x) = x \) to \( f(3x) \) compresses the graph horizontally.
• The transformation from \( f(3x) \) to \( f(3x) - \frac{1}{3} \) shifts the graph down.

Thus, the correct answer is: Compressed horizontally and shifted down.