Graph f (x) = tan 3x. Identify period, x-intercepts and asymptotes

Well the period of the tan (x) function is π. It means that when you add π on X axis you will get the same y axis value.

There is a little trick to find the period of functions like yours.

You just divide period of basic tan (x) function with, in your case 3.

So this mean you have

To = π/3

Function intercepts x axis when function is equal to 0.

tan (3x) = 0

3x = k * π

x = k * (π / 3)

There are only vertical asymptotes in tangent function.

You can easily see it if you look at the graph

tan (x) = ∞, (π/2 + kπ)

tan (x) = - ∞ (-π/2 + kπ).

x = π/2 + kπ

x = - π/2 + kπ

tan (3x) = ∞

3x = π/2 + kπ

x = π/6 + kπ/3

tan (3x) = - ∞

3x = - π/2 + kπ

x = - π/6 + kπ/3