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Math Help - Function Transformations

  1. #1
    Member cassiopeia1289's Avatar
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    Function Transformations

    ok, I know this is a basic, but I have completely forgot

    If f(x)= x^2 - 1, describe in words what the following would do to the graph of f(x):

    abs(f(x))

    and also, they've drawn a graph with cordinates and they tell you to transform it so that y=f(abs(x))

    please please please help!
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  2. #2
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    Can you answer the question from this graph?
    Attached Thumbnails Attached Thumbnails Function Transformations-grp_ab.gif  
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  3. #3
    Member cassiopeia1289's Avatar
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    but is abs(f(x)) different than f(abs(x)) cause the worksheet seems to think so

    also, how would one describe that in words?? lol ...
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  4. #4
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    This is a differrent function. Study it.
    Can you see what is going on?
    Attached Thumbnails Attached Thumbnails Function Transformations-grp_ab1.gif  
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  5. #5
    Member cassiopeia1289's Avatar
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    wait, ok, so it shifts everything up so its positive
    but whats the difference in the absolute value of the entire f(x) verses f(abs(x))?

    so if you had a figure with cordinates like (-4, 0) (0,2) (1,0) (2,-2) (3,0)
    and you wanted to make it f(abs(x)) and also abs(f(x)) how would you do that? would you make that dropped down V positive and disconnect the lines and points?

    wait, ok, I get the f(abs(x)) (make the negative reflect off of axis)
    but the abs(f(x)), how is that different?
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  6. #6
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    Quote Originally Posted by cassiopeia1289 View Post
    whats the difference in the absolute value of the entire f(x) verses f(abs(x))?
    Think of the y-axis as a miror. It just copies the positive x-side.
    Attached Thumbnails Attached Thumbnails Function Transformations-grp_ab2.gif  
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  7. #7
    Member cassiopeia1289's Avatar
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    could you possible just give me the answer, I'm one of those people that goes backwards and teaches myself, that's the way I run, weird I know, but I just need the difference between the two and then I'll try and figure it
    but the figure I need is more like a star connection, ya know? its not the swoopy line, I get those, but its lines connected by dots
    Last edited by ThePerfectHacker; August 12th 2007 at 03:53 PM.
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  8. #8
    Member cassiopeia1289's Avatar
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    ok, I take it back, could you sketch a connected dot figure just plainly, then do y=f|x| to the graph and then seperately do y=|f(x)|
    also, how do you know which side to reflex?
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  9. #9
    Member cassiopeia1289's Avatar
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    I take all of it back, |f(x)| makes everything have to be positive so it flips and f|(x)| is the mirror one, right???
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  10. #10
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    Now that you have done some work (thought) on your own, I can help you more.
    Once we have a graph of f(x) then because \left| x \right| \ge 0 then the whole graph of f\left( {\left| x \right|} \right) just looks like the right-hand (the positive side of the y-axis, the first and fourth quadrants).

    Example: for every x it is true that f\left( {\left| x \right|} \right) = f\left( {\left| { - x} \right|} \right).

    So just copy the right-hand of the graph to the left-hand letting the y-axis act as a mirror.
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