Which of the following correctly identifies the transformations undergone from f(x)=x

Question

to f(3x)−13 =3x−13
(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 \( f(3x) - 13 = 3x - 13 \), we can break it down into steps:

1. Start with the function:

   • \( f(x) = x \)

2. Apply the transformation \( f(3x) \):

   • This transformation involves substituting \( 3x \) in place of \( x \).
   • The function now becomes \( f(3x) = 3x \).
   • This represents a horizontal compression by a factor of 3 (because we are multiplying \( x \) by 3).

3. Then apply \( f(3x) - 13 \):

   • Now we subtract 13 from the result: \( 3x - 13 \).
   • This corresponds to a vertical shift downward of 13 units.

Conclusion: The overall transformation from \( f(x) = x \) to \( f(3x) - 13 = 3x - 13 \) consists of a horizontal compression by a factor of 3 and a vertical shift downward by 13 units.

The correct answer is: compressed horizontally and shifted down.