Question

Transformation of function f(x) = 3ˣ to y = (1/3)(3^(-2x+4))+1:

Describe the sequence of transformations.
(A) Reflection in the x-axis, compression, translation up
(B) Reflection in the y-axis, stretch, translation down
(C) Stretch, translation right, reflection in the x-axis
(D) Compression, translation left, reflection in the y-axis

Answer 1

The transformation sequence for f(x) = 3^x to y = (1/3)(3^(-2x+4)) + 1 is a compression by a factor of 1/3, followed by a reflection in the y-axis due to the negative sign in the exponent, and concluded by a translation upward by one unit.

Step-by-step explanation:

When examining the transformation of the function f(x) = 3x to y = (1/3)(3-2x+4) + 1, we can identify the sequence of transformations by looking at the changes to the base function. Firstly, there is a compression by a factor of 1/3 due to the scalar multiple in front of the base function. Next, a reflection in the y-axis is observed because of the negative sign in the exponent (-2x). Lastly, the function is translated up by +1, as evident from the addition outside the function.

To summarize, the sequence of transformations is:

1. Compression by a factor of 1/3 (vertical compression).
2. Reflection in the y-axis because the x in the exponent is multiplied by -1.
3. Translation up by 1 unit.