“one-third of a number, decreased by 6, equals 11.”
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Answer:
y = cot(x - ⅓π) + 2
Step-by-step explanation:
The general equation for a cotangent function with the given properties is
y = Acot(Bx + C) + D, where
A = the stretching factor
π/|B| = the period
C = the phase shift (negative is to the right)
D = the vertical shift
A = 1
π/|B| = π, so1/|B| = 1 and B = 1
C = -⅓π
D = 2
The function is
y = cot(x - ⅓π) + 2
The figure below shows the graph of the function with the given parameters.
Note that the parent function y = cot(x) has the y-axis as an asymptote, so we can measure the phase shift by the movement of the asymptote π units to the right.
