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

Answer 1

To analyze the transformations from \( f(x) = x \) to \( f(3x) - 13 = 3x - 13 \), we can break it down step by step.

1. Starting Function: \( f(x) = x \)

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

   • The transformation from \( f(x) \) to \( f(3x) \) involves compressing the function horizontally by a factor of 3. This happens because \( f(kx) \) compresses the graph horizontally by a factor of \( k \).

3. Then Transforming \( f(3x) \) to \( f(3x) - 13 \):

   • Subtracting 13 from the function shifts the entire graph down by 13 units.

Taking these transformations into account, the overall transformation from \( f(x) = x \) to \( f(3x) - 13 \) is that the graph is compressed horizontally and shifted down.

Therefore, the correct response is:

compressed horizontally and shifted down.