# How do you graph y=-3cot(1/2(x+pi))-1?

Jun 16, 2018

As below.

#### Explanation:

$\text{Standard form of cotangent function } y = A \cot \left(B x - C\right) + D$

$y = - 3 \cot g r a p h \left\{- 3 \cot \left(\frac{x}{2} + \frac{\pi}{2}\right) - 1 \left[- 10 , 10 , - 5 , 5\right]\right\} \left(\frac{x}{2} + \frac{\pi}{2}\right) - 1$

$A = - 3 , B = \frac{1}{2} , C = - \frac{\pi}{2} , D = - 1$

$A m p l i t u \mathrm{de} = | A | = \text{NONE for cotangent function}$

"Period = pi / |B| = pi / (1/2) = 2pi

$\text{Phase Shift " = -C / B = (pi/2)/(1/2) = pi, pi " to the right}$

$\text{Vertical Shift } = D = - 1$