Respuesta :
Answer:
C. A horizontal stretch to produce a period of [tex]2\pi[/tex] and a vertical compression.
Step-by-step explanation:
We are given the parent function as [tex]y= \cot x[/tex]
It is given that, transformations are applied to the parent function in order to obtain the function [tex]y=0.5\cot (0.5x)[/tex] i.e. [tex]y=\frac{1}{2}\cot (\frac{x}{2})[/tex]
That is, we see that,
The parent function [tex]y= \cot x[/tex] is stretched horizontally by the factor of [tex]\frac{1}{2}[/tex] which gives the function [tex]y=\cot (\frac{x}{2})[/tex].
Further, the function is compressed vertically by the factor of [tex]\frac{1}{2}[/tex] which gives the function [tex]y=\frac{1}{2}\cot (\frac{x}{2})[/tex].
Now, we know,
If a function f(x) has period P, then the function cf(bx) will have period [tex]\frac{P}{|b|}[/tex].
Since, the period of [tex]y= \cot x[/tex] is [tex]\pi[/tex], so the period of [tex]y=\frac{1}{2}\cot (\frac{x}{2})[/tex] is [tex]\frac{\pi}{1/2}[/tex] = [tex]2\pi[/tex]
Hence, we get option C is correct.
