Which of the following correctly identifies the transformations undergone from f(x)=x to f(3x)−13 =3x−13. Select all that apply

Question

(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 into steps:

1. Start with \( f(x) = x \).
2. Apply the transformation \( f(3x) \): The function \( f(3x) \) compresses the graph horizontally by a factor of 3. This means that the inputs are scaled by 1/3, making the graph steeper.
3. Then, apply the transformation \( -13 \): The term \( -13 \) shifts the graph down by 13 units.

Now, let's look at the options:

1. Compressed horizontally and shifted down – Correct.

   • The transition from \( f(x) \) to \( f(3x) \) compresses the graph horizontally, and the subtraction of 13 shifts it down.

2. Reflected over the y-axis and shifted up – Incorrect.

   • There is no reflection over the y-axis, and it shifts down not up.

3. Stretched horizontally and shifted down – Incorrect.

   • The graph is compressed horizontally, not stretched.

4. Reflected over the x-axis and shifted up – Incorrect.

   • There is no reflection over the x-axis, and it is shifted down not up.

The only correct option is:

• Compressed horizontally and shifted down.