**To produce the graph of the function y=0.5cot(0.5x), what transformations should be applied to the graph of the parent function y=cot(x)?** We have prepared the options and answers on this subject for you. Here you go, let’s examine it together.

**To produce the graph of the function Y=0.5cot(0.5x)**

**To produce the graph of the function y=0.5cot(0.5x), what transformations should be applied to the graph of the parent function y=cot(x)?**

**a)**a horizontal compression to produce a period of pi/2 and a vertical compression**b)**a horizontal compression to produce a period of pi/2 and a vertical stretch**c)**a horizontal stretch to produce a period of 2pi and a vertical compression**d)**a horizontal stretch to produce a period of 2pi and a vertical stretch

**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

- It is given that, transformations are applied to the parent function in order to obtain the function i.e.

- 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 =

**We get option C is correct.** That’s it to produce the graph of the function Y=0.5cot(0.5x). We hope you understand. We wish you pleasant work.