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 \( f(3x) - 13 = 3x - 13 \), let's break it down:

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

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

   • The function \( f(3x) = 3x \) involves multiplying the input \( x \) by 3. This transformation compresses the graph horizontally by a factor of 3, meaning it will appear "narrower".

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

   • Next, we subtract 13 from the entire function. This shifts the graph down by 13 units.

Combining these transformations, we can conclude that from \( f(x) = x \) to \( f(3x) - 13 = 3x - 13 \), the function undergoes a horizontal compression and a downward shift.

Therefore, the correct response is:

• compressed horizontally and shifted down.