Question

Which of the following correctly identifies the transformations undergone from f (x) = z to (3x) - 1/3 = 3x - 1/3 (1 point)
compressed horizontally and shifted down
reflected over the y-axis and shifted up
stretched horizontally and shifted down
reflected over the x-axis and shifted up

Answer 1

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**.