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

To analyze the transformation from the function \( f(x) = z \) (which we can assume is the identity function \( f(x) = x \)) to \( g(x) = 3x - \frac{1}{3} \), we can break it down as follows:

1. Identifying the base function: Start with \( f(x) = x \).
2. Horizontal Scaling: The function \( g(x) = 3x - \frac{1}{3} \) has a coefficient of 3 in front of \( x \). This indicates a vertical stretch by a factor of \( \frac{1}{3} \) (this is actually a horizontal compression) because the graph is compressed horizontally (the effects of horizontal scaling change if the function is in the form \( kf(x) \)).
3. Vertical Shift: The term \(-\frac{1}{3}\) translates the graph downward by \(\frac{1}{3}\).

Combining these transformations, the correct description becomes:

• The function is compressed horizontally (due to the factor of 3) and shifted down (due to the \(-\frac{1}{3}\) term).

Thus, the correct option is: compressed horizontally and shifted down.