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

Question

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

Answer 1

To analyze the transformation from \( f(x) = x \) to \( f(3x) - \frac{1}{3} \), we will go step-by-step:

1. Start with \( f(x) = x \).
2. Transform to \( f(3x) \):
   • The function becomes \( f(3x) = 3x \).
   • This represents a horizontal compression by a factor of \( \frac{1}{3} \).
3. Then shift down by \( \frac{1}{3} \):
   • The transformation results in \( f(3x) - \frac{1}{3} = 3x - \frac{1}{3} \).

Given these transformations:

• The function is compressed horizontally (due to the factor of 3 in \( f(3x) \)).
• It is also shifted down by \( \frac{1}{3} \).

Therefore, the correct identification of the transformations is:

• Compressed horizontally and shifted down.