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 + }(\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{ = }(\pi)/(1)\text{ = }\pi`

Therefore, the Period is π.

For the Phase Shift:

`\text{ Phase Shift = }\frac{\text{ c}}{\text{ b}}\text{ = }(-(\pi)/(6))/(1)\text{ = -}(\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: