Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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

Sagot :

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