Question

) Which of the following correctly identifies the transformations undergone from f(x) = x to
f(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 identify the transformations undergone 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 \( f(3x) \)**:
- The expression \( f(3x) \) indicates a horizontal compression. Specifically, \( x \) is replaced with \( 3x \), which compresses the graph horizontally by a factor of 3.

3. **Transformation to \( 3x \)**:
- The function is multiplied by 3, indicating a vertical stretch by a factor of 3.

4. **Transformation to \( 3x - \frac{1}{3} \)**:
- Finally, we subtract \( \frac{1}{3} \), which means the graph is shifted down by \( \frac{1}{3} \).

Putting all of this together, we can conclude that the transformations are:

- Compressed horizontally by a factor of 3 (due to \( f(3x) \)).
- Stretched vertically by a factor of 3 (due to the multiplication by 3).
- Shifted downward by \( \frac{1}{3} \) (due to the subtraction of \( \frac{1}{3} \)).

The correct answer among the options you provided is:

**compressed horizontally and shifted down.**