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 \( f(3x) - 13 = 3x - 13 \), let's break it down:

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

2. **Transformation to \( f(3x) \)**:
- The function \( f(3x) = 3x \) involves multiplying the input \( x \) by 3. This transformation compresses the graph horizontally by a factor of 3, meaning it will appear "narrower".

3. **Transformation to \( f(3x) - 13 \)**:
- Next, we subtract 13 from the entire function. This shifts the graph down by 13 units.

Combining these transformations, we can conclude that from \( f(x) = x \) to \( f(3x) - 13 = 3x - 13 \), the function undergoes a **horizontal compression** and a **downward shift**.

Therefore, the correct response is:

- **compressed horizontally and shifted down**.