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26 May, 06:28

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

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  1. 26 May, 06:34
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    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
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