Question

If given the graph of 𝑓(𝑥) = − sin (3x + 𝜋/3 ) − 2 describe the steps you would take to draw the graph of the reciprocal function

Answer 1

let's graph the original function

http://www.wolframalpha.com/input/?i=plot+y++%3D+%E2%88%92+sin+(3x+%2B+%CF%80%2F3+)+%E2%88%92+2

Notice that the curve does not cross or touch the x-axis, that is , it can never be zero.
Therefore the reciprocal can never be undefined and will be continuous.

I assume you know how to sketch a reciprocal curve for a given function.

Here is a graph of both functions, the reciprocal is in red

http://www.wolframalpha.com/input/?i=plot+y++%3D+%E2%88%92+sin+(3x+%2B+%CF%80%2F3+)+%E2%88%92+2,+y+%3D+1%2F(%E2%88%92+sin+(3x+%2B+%CF%80%2F3+)+%E2%88%92+2)