The transformation of a function may lead to the rigid motion based on what type of transformation you applied in it. Thus, option D is correct.
We need to check the transformation that is the rigid motion for the function f(x).
Now, the different transformation is given below:
- 2f(x)+3,
- f(x/2)+1,
- 2f(x/2),
- f(x-1/2)+3
Let us take the transformations of the function from the top to the bottom.
(1) In the first transformation, we changed our function f(x) to 2f(x)+3.
When we used multiplication of division operations towards any functions then it will change the amplitude of the function, and hence it is not a rigid motion.
(2) In the second transformation, we changed our function f(x) to f(x/2)+1.
When we used multiplication of division operations towards any functions then it will change the amplitude of the function, and hence it is not a rigid motion.
(3) In the third transformation, we changed our function f(x) to 2f(x/2).
When we used multiplication of division operations towards any functions then it will change the amplitude of the function, and hence it is not a rigid motion.
(4) In the fourth transformation, we changed our function f(x) to f(x-1/2)+3.
When we used multiplication of division operations towards any functions then it will change the amplitude of the function, and when we use addition or subtraction towards any function then the amplitude remains constant. Hence, it is a rigid motion.
Thus, option D is correct.
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