Answer:
C. A horizontal stretch to produce a period of
and a vertical compression.
Step-by-step explanation:
We are given the parent function as ![y= \cot x](https://tex.z-dn.net/?f=y%3D%20%5Ccot%20x)
It is given that, transformations are applied to the parent function in order to obtain the function
i.e. ![y=\frac{1}{2}\cot (\frac{x}{2})](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D%5Ccot%20%28%5Cfrac%7Bx%7D%7B2%7D%29)
That is, we see that,
The parent function
is stretched horizontally by the factor of
which gives the function
.
Further, the function is compressed vertically by the factor of
which gives the function
.
Now, we know,
If a function f(x) has period P, then the function cf(bx) will have period
.
Since, the period of
is
, so the period of
is
= ![2\pi](https://tex.z-dn.net/?f=2%5Cpi)
Hence, we get option C is correct.