Answer:
[tex]y=7\csc{\left(\dfrac{x}{2}\right)}-2[/tex]
Step-by-step explanation:
The range of a cosecant function normally excludes the interval (-1, 1). Yours excludes the interval (-9, 5), which has a width 7 times as great. Thus we know the vertical scale factor is 7.
The midpoint of the excluded interval of your function is (-9+5)/2 = -2, so that is the vertical translation.
The cosecant function normally has vertical asymptotes at x=0 and x=π, so your function is expanded horizontally by a factor of 2.
Your cosecant function is ...
[tex]\boxed{y=7\csc{\left(\dfrac{x}{2}\right)}-2}[/tex]
