Question

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Answer 1

Answer:

$\displaystyle y = cot(x - \frac{π}{3}) + 2$

Explanation:

See above graph

$\displaystyle y = Acot(Bx + C) + D \\ \\ Amplitude → |A| \\ Period → \frac{π}{B} \\ Phase\:[Horisontal]\:Shift → \frac{C}{B} \\ Vertical\:Shift → D$

* The cotangent sinusoidal equation is the ONLY equation that will have a C instead of −C:

$\displaystyle y = Asin(Bx - C) + D \\ y = Acos(Bx - C) + D \\ y = Atan(Bx - C) + D \\ y = Asec(Bx - C) + D \\ y = Acsc(Bx - C) + D \\ y = Acot(Bx + C) + D$

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Answer 2

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.