Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.

y=csc (x) -9

The answer is vertical translation down 9 units  ⇒ answer (d)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) - k

* Lets study the problem

- The basic function is y = csc(x)

∵ y = csc(x) - 9

- That means the function translated vertically 9 units down

* Vertical translation 9 units down

* Look to the graph

-The red graph is y = csc(x)

- The green graph is y = csc(x) - 9