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?

Guest Mar 19, 2020

#1**+3 **

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

And

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

CPhill Mar 19, 2020