The parent cosecant function is shifted 2units down, and it's period is changed to 6π. Which of the following is the graph of the transformed function?

The function of the graph of y = cscx after the graph is shifted down 2 units and it's period is changed to 6π is y = csc(x/3)-2. This is obtained by using rules of transformation of function.

What are the Rules of Transformation of Function?

Rules of transformation of linear function are

f(x)+b - function is shifted b units upward

f(x)-b - function is shifted b units downward

f(x+b) - function is shifted b units to the left

f(x-b) - function is shifted b units to the right

-f(x) - function is reflected over x-axis

f(-x) - function is reflected over y-axis

y=sin (kx), where period=2π/k

Find the function required:

Given that the function is y=cscx

First the graph is shifted down 2 units

By the transformation we can rewrite the function in f(x)-b form;

that is ⇒ y = cscx-2

Next the period is changed to 6π

We can say that, 6π=2π/k ⇒k=2π/6π ⇒k=1/3

putting in the function ⇒ y=csc(x/3)-2

This is the required function.

Hence the function of the graph of y=cscx after the graph is shifted down 2 units and it's period is changed to 6π is y = csc(x/3)-2.

Learn more about transformation rules of trigonometric functions here:

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