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Math Help - Step function Graphing issue

  1. #1
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    Step function Graphing issue

    Okay, I'm slightly confused. I'm currently in the beginning of my course Algebra 2 /Trig and I can't seem to figure out how to graph this step function

    2[[x+5]]

    I'm comfortable with rigid transformations, but this seems to be nonrigid?

    Help. Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Skynt View Post
    Okay, I'm slightly confused. I'm currently in the beginning of my course Algebra 2 /Trig and I can't seem to figure out how to graph this step function

    2[[x+5]]

    I'm comfortable with rigid transformations, but this seems to be nonrigid?

    Help. Thanks.

    I'm afraid your notation means nothing to me. Please explain what [[z]] is
    meant to denote. Presumably from the title of this thread it is supposed
    to denote the Heaviside unit step function.

    RonL
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  3. #3
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    Well. it's the Greatest Integer notation I think. I know a function that uses it forms steps on a graph.
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  4. #4
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    The greatest integer function is also known as the floor function.
    Attached Thumbnails Attached Thumbnails Step function Graphing issue-step.gif  
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  5. #5
    MHF Contributor kalagota's Avatar
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    i'll try to explain it with this..
    consider the graph of
    y = [|x|], i assume you know the graph of this basic function..

    now, the effects on that graph when you have the general form of the greatest integer function
    y = a[|bx - c|] + d is this..

    \frac{1}{b} is the length of each step

    \frac{c}{b} horizontal shift of the graph

    a is the distance between steps.. (because of the effect of this part, the "slope" of the "ladder" is more positive if a>1, while the slope approaches to 0 when 0<a<1)

    d is the value of y when on the interval \left[ \frac{c}{b},\frac{c + 1}{b} \right)

    thus, from your given 2[|x + 5|],

    the graph of y=[|x|] shifts 5 units to the left and the distance between steps is 2..
    Attached Thumbnails Attached Thumbnails Step function Graphing issue-effects_of_gif.jpg  
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by Skynt View Post
    Well. it's the Greatest Integer notation I think. I know a function that uses it forms steps on a graph.
    This is the floor function usually written \lfloor x \rfloor.

    RonL
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