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.