SOLUTION: Give the amplitude, vertical shift, phase shift, and period for the equation. y = -2cot(4x-24pi)+1

Question 578596: Give the amplitude, vertical shift, phase shift, and period for the equation.
y = -2cot(4x-24pi)+1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Give the amplitude, vertical shift, phase shift, and period for the equation.
y = -2cot(4x-24pi)+1
**
Equation for graphing cot function: y=Acot(Bx-C), Period=π/B, Phase shift=C/B.
For given equation:
Vertical shift=1
period=π/B=π/4≈.785 radians
phase shift=C/B=24π/4=6π (to the right)
The coefficient 2 stretches the curve vertically
The negative sign means that the curve is reflected about the x-axis
There is no maximum or minimum like sin and cos curves; only asymptotes at the beginning and end of the period. Since the curve was shifted 6π radians, there are asymptotes at x≈19.63 and 18.85 (for one period)
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