Question

Which of the following correctly identifies the transformations undergone from f(x)=x
to f(3x)−13 =3x−13
(1 point)
Responses

compressed horizontally and shifted down
compressed horizontally and shifted down

reflected over the y-axis and shifted up
reflected over the y -axis and shifted up

stretched horizontally and shifted down
stretched horizontally and shifted down

reflected over the x-axis and shifted up
reflected over the x -axis and shifted up

Answer 1

To analyze the transformation from \( f(x) = x \) to \( f(3x) - 13 = 3x - 13 \), we can break it down into steps:

1. **Start with the function:**
- \( f(x) = x \)

2. **Apply the transformation \( f(3x) \):**
- This transformation involves substituting \( 3x \) in place of \( x \).
- The function now becomes \( f(3x) = 3x \).
- This represents a **horizontal compression** by a factor of 3 (because we are multiplying \( x \) by 3).

3. **Then apply \( f(3x) - 13 \):**
- Now we subtract 13 from the result: \( 3x - 13 \).
- This corresponds to a **vertical shift downward** of 13 units.

**Conclusion:**
The overall transformation from \( f(x) = x \) to \( f(3x) - 13 = 3x - 13 \) consists of a horizontal compression by a factor of 3 and a vertical shift downward by 13 units.

The correct answer is:
**compressed horizontally and shifted down.**