The range of a cosecant function is (-∞,-9] ∪ [5,∞). The equations of two consecutive asymptotes of the function are x = 0 and x=2π. The function is not a reflection over the x-axis.
What is the equation of this cosecant function?
The form we seek is
y = Acsc ( Bx) + C
A = the amplitude = [5 - - 9] / 2 = 14/ 2 = 7
C = the midline = [ 5-9]/2 = -4/2 = -2
The period = 2pi - 0 = 2pi
B = normal period / our period = pi / [ 2pi] = 1/2
So....our equation is
y = 7csc ( (1/2)x) - 2
Here's the graph : https://www.desmos.com/calculator/qpwj6t9ook
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