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

1. Transformation to \( f(3x) \):

   • The transformation from \( f(x) = x \) to \( f(3x) \) is a horizontal compression by a factor of 3. This is because the function is being evaluated at a value \( 3x \), which means inputs are scaled by a factor of 3, resulting in the graph being "squeezed" horizontally.

2. Transformation to \( f(3x) - 13 \):

   • The next transformation is the subtraction of 13, which shifts the function down by 13 units.

Putting this all together:

• The function goes from being \( f(x) = x \) to \( f(3x) \), which compresses it horizontally, and then to \( f(3x) - 13 \), which shifts it down.

Therefore, the correct identification of the transformations undergone from \( f(x) = x \) to \( f(3x) - 13 \) is:

Compressed horizontally and shifted down.