Question

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

Multiple choice
Responses:

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 transformations from \( f(x) = x \) to \( f(3x) - \frac{1}{3} = 3x - \frac{1}{3} \), let's break down the transformations step by step:

1. **Start with** \( f(x) = x \).
2. **Transform to** \( f(3x) \):
- This represents a **horizontal compression** by a factor of 3. The function \( f(3x) \) compresses the graph horizontally because the input values are scaled by a factor of \( \frac{1}{3} \).

3. **Then apply** \( -\frac{1}{3} \):
- After obtaining \( f(3x) = 3x \), we then have \( f(3x) - \frac{1}{3} \). This operation shifts the entire graph **down by \( \frac{1}{3} \)**.

Combining these transformations, we find that the correct identification is:

**Compressed horizontally and shifted down**.

So the correct choice is:
- **compressed horizontally and shifted down**.