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Math Help - types of funtions

  1. #1
    Member Rimas's Avatar
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    types of funtions

    i am having trouble filling out the chart of basic functions that includes periodic and one by one

    i dont understand the concept


    X^2
    X^3
    Abs(x)
    Sin(x)
    Cos(x)
    Tan(x)
    Sec(x)
    2^x
    Logbase 2 of x
    1/x
    Sq rt of X
    sq rt of a^2- x^2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rimas View Post
    i am having trouble filling out the chart of basic functions that includes periodic and one by one

    i dont understand the concept


    X^2
    X^3
    Abs(x)
    Sin(x)
    Cos(x)
    Tan(x)
    Sec(x)
    2^x
    Logbase 2 of x
    1/x
    Sq rt of X
    sq rt of a^2- x^2
    i suppose you mean one to one?

    intuitively, a function is periodic if it has a repeating pattern, forever. sin(x) is obviously one. it's period is 2 \pi. you have the same pattern between [0, 2 \pi] repeating forever.

    slightly more formally, a function f(x) is called periodic, if f(x) = f(x + kT) for some integer k. we call T the period.

    for example, going back to sine. \sin x = \sin (x + 2k \pi), the period is T = 2 \pi. any multiple of the period and you get back the same value. so \sin x = \sin (x + 2 \pi) = \sin (x + 6 \pi) = \sin (x - 12 \pi) etc


    a function is called one-to-one if f(x_1) = f(x_2) \implies x_1 = x_2. or equivalently, x_1 \ne x_2 \implies f(x_1) \ne f(x_2) for x_1, x_2 \in \text{dom}(f)
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