Question

I need help with this practice problem It is from my ACT prep guide It asks to graph the function, if you can, use Desmos to complete

Answer 1

Given the following function:

$\text{ f(x) = cot(x + }\frac{\pi}{6})$

Use the form a·cot(bx - c) to find the variables used to find the amplitude, period, phase shift and vertical shift.

We get,

a = 1

b = 1

c = -π/6

d = 0

Since the graph of the Cotangent function does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

For the Period:

$\text{ Period = }\frac{\text{ }\pi}{\text{ b}}\text{ = }\frac{\pi}{1}\text{ = }\pi$

Therefore, the Period is π.

For the Phase Shift:

$\text{ Phase Shift = }\frac{\text{ c}}{\text{ b}}\text{ = }\frac{-\frac{\pi}{6}}{1}\text{ = -}\frac{\pi}{6}$

Therefore, Phase Shift is -π/6 → π/6 (To the left).

For the Vertical Shift:

Vertical Shift = 0

Plotting the function will be: