Question

Which of the following correctly identifies the transformations undergone from f(x)=x to f(3x)−13 =3x−1/3 (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 \( f(3x) - 13 = 3x - \frac{1}{3} \), we can break it down step by step.

1. Start with \( f(x) = x \): This is our original function.

2. Transform to \( f(3x) \):

   • Changing \( x \) to \( 3x \) compresses the function horizontally by a factor of 3.

3. Transform to \( f(3x) - 13 \):

   • The subtraction of 13 shifts the function down by 13 units.

Combining these transformations, the function \( f(x) = x \) is first compressed horizontally by a factor of 3 due to \( f(3x) \), and then it is shifted down by 13 units due to the \( -13 \) adjustment.

Thus, the correct identification of the transformations is:

Compressed horizontally and shifted down.