Explain how the graph of y = 2csc(x - pi/4) - 5 is related to the graph of the basic trigonometric function y = cscx.
1 answer:
Answer: The distance between the min and max increased by a factor of 2, horizontally shifted to the right by , shifted down 5 units, and has a phase shift of
<u>Step-by-step explanation:</u>
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-axis
- C is a horizontal shift (left or right)
- D is a vertical shift (up or down)
- Period is
- Phase Shift is
In the given transformed graph y = 2 csc (x - ) - 5
- A = 2 --> distance between the Min and max is 2(2) = 4
- C =
--> horizontally shifted to the right
- D = -5 --> shifted DOWN 5 units
- Phase shift is
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