Question

Question #1a9c9

Answer 1

The period is `pi/3`, and the asymptotes are at `pi/3, -pi/3, pi, -pi`.

Explanation:

The standard form of a cotangent function is `f(x)=a cot (bx-c) +d`.

The period of a tangent or cotangent function is equal to `pi/(absb)`. (On the other hand, the period of a sine, cosine, cosecant, or secant function is equal to `(2pi)/(absb)`.)

In this case, `b=3`.

`pi/(absb) = pi/(abs3) = pi/3`

Additionally, the function `cot x` has asymptotes at `x=pin, n in Z`. However, since `f(x) = 2 cot 3x` is horizontally shrunk by a factor of `1/3`, the asymptotes are at `x=pi/3n, n in Z`. So, the asymptotes would be at `pi/3, -pi/3, pi, -pi`.