Explain how the graph of y = 2csc(x - pi/4) - 5 is related to the graph of the basic trigonometric function y = cscx.

Answer: The distance between the min and max increased by a factor of 2, horizontally shifted to the right by [tex]\bold{\dfrac{\pi}{4}}[/tex], shifted down 5 units, and has a phase shift of [tex]\bold{\dfrac{\pi}{4}}[/tex]Step-by-step explanation:The general form of a csc function is: y = A csc (Bx - C) + D  where|A| is the amplitude (vertical stretch) -A is a reflection over the x-axis|B| is the horizontal stretch-B is a reflection over the y-axisC is a horizontal shift (left or right)D is a vertical shift (up or down)Period is [tex]\dfrac{2\pi}{B}[/tex]Phase Shift is [tex]\dfrac{C}{B}[/tex]In the given transformed graph y = 2 csc (x - [tex]\dfrac{\pi}{4}[/tex]) - 5A = 2   --> distance between the Min and max is 2(2) = 4C = [tex]\dfrac{\pi}{4}[/tex]  --> horizontally shifted to the right  [tex]\dfrac{\pi}{4}[/tex] unitsD = -5  --> shifted DOWN 5 unitsPhase shift is [tex]\dfrac{\pi}{4}[/tex]