The range of a cosecant function is (-inifnity symbol, -9] U [5, infinity symbol). The equations of two consecutive asymptotes of the function are x=0 and x=2pi. The function is not a reflection over the x-axis.
What is the equation of this cosecant function?
The midline of this function is y = [ -9 + 5 ] / 2 = -4/2 = -2
The amplitude of the function is abs value ( [-9 -5] /2) = abs value (-14/2 ) =abs value (-7) = 7
The period is twice as long as the regular csc function
The equation is
y = 7 csc (x/2) - 2
Here's the graph : https://www.desmos.com/calculator/uy4w9njnon