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 \( f(3x) - 13 \):

1. Start with \( f(x) = x \): This is the identity function.
2. Transform to \( f(3x) \):
   • Replacing \( x \) with \( 3x \) in \( f(x) \) results in a horizontal compression by a factor of 3. This means that the graph is compressed towards the y-axis.
3. Then apply \( -13 \):
   • Subtracting 13 from the function shifts the entire graph downward by 13 units.

Putting these transformations together, the final transformation from \( f(x) = x \) to \( f(3x) - 13 \) involves a horizontal compression and a downward shift.

Therefore, the correct response is:

compressed horizontally and shifted down.