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Math Help - f(x+5) = f(x)

  1. #1
    Member
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    Smile f(x+5) = f(x)

    The figure above shows a portion of the graph of the function f. If f(x+5) = f(x) for all values of x, then f(x) = 0 for how many different values of x between 0 and 12?

    http://img187.imageshack.us/img187/4666/dsc00054i.jpg

    a. 8
    b. 9
    c. 10
    d. 11
    e. 12

    thanks

    also whats a period graph of function? hows it related to the question?

    thanks
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Periodic function

    Hello aeroflix
    Quote Originally Posted by aeroflix View Post
    The figure above shows a portion of the graph of the function f. If f(x+5) = f(x) for all values of x, then f(x) = 0 for how many different values of x between 0 and 12?

    http://img187.imageshack.us/img187/4666/dsc00054i.jpg

    a. 8
    b. 9
    c. 10
    d. 11
    e. 12

    thanks

    also whats a period graph of function? hows it related to the question?

    thanks
    A periodic function is one whose values are repeated at regular intervals or periods. On the graph of the function, the period itself is the horizontal distance between two consecutive corresponding points.

    If f is such that f(x+5) = f(x) for all values of x then f is periodic with period 5. This means that the graph repeats every 5 units horizontally.

    To find where f(x) = 0, we need to know where the graph crosses the x-axis. Between x = 0 and x = 5, the graph cuts the x-axis 4 times; so it will cut it another 4 times between 5 and 10. (That's 8 so far.)

    Between 0 and 2, the graph crosses the x-axis just once; so it will cross once between 10 and 12.

    So there are 9 values of x between 0 and 12 altogether.

    Grandad
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  3. #3
    Senior Member pacman's Avatar
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    from 1 to 5 : 4
    from 6 to 10 : 4
    from 11 to 12 : 1

    4 + 4 + 1 = 9
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