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Math Help - How to solve this function

  1. #1
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    How to solve this function

    a function f is defined by:

    0 (x<-1)
    x+1 (-1<x<1)
    f(x)= 1-x (0<x<1)
    0 (x>1)

    Sketch on separate daiagrams the graphs of f(x)
    f(x+0.5), f(x+1), f(x+2), f(x-0.5), f(x-1 and f(x-2)
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  2. #2
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    skeeter's Avatar
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    Re: How to solve this function

    Quote Originally Posted by leketapis View Post
    a function f is defined by:

    0 (x<-1)
    x+1 (-1<x<1)
    f(x)= 1-x (0<x<1)
    0 (x>1)

    Sketch on separate daiagrams the graphs of f(x)
    f(x+0.5), f(x+1), f(x+2), f(x-0.5), f(x-1 and f(x-2)
    sketch the piece-wise function of f(x)

    f(x+c) involves a horizontal shift of f(x) c units to the right or left ... your notes/text should indicate which way.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: How to solve this function

    Quote Originally Posted by The Chaz
    1. It's a piecewise-defined function, and there's no way I'm drawing this for you! Maybe someone else will... but I would recommend that you learn how to graph piecewise functions. Basically, for all the different ways that f is defined

    (in this case,
    0,
    x + 1, and
    1 - x)

    2. Draw the lines
    y = 0
    y = x + 1 and
    y = 1 - x on the same set of coordinate axis. In pencil.

    3. Use a colored pencil (or heavier hand) to emphasize the line y = 0 for the part of this line where x < -1 (as defined in your example).
    Use a colored pencil (or heavier hand) to emphasize the line y = x + 1 for the part of this line where -1 < x < 0 (as defined in your example).
    I changed it to "0", because otherwise your function is not well-defined.

    Use a colored pencil (or heavier hand) to emphasize the line y = 1 - x for the part of this line where 0 < x < 1 (as defined in your example).
    Use a colored pencil (or heavier hand) to emphasize the line y = 0 for the part of this line where x > 1 (as defined in your example.

    Also, you'll have to determine how to define f(-1), f(0), and f(1) by looking for ≤ or ≥ in your original problem. Another guess of mine is that you omitted these.

    Now, erase everything that you didn't highlight in step 3.

    viola.

    The second part is asking for transformations of this graph. This next sentence will tell you everything you need to know.

    The graph of f(x - h) is the graph of f(x), shifted right "h" units.

    http://www.mymathforum.com/viewtopic...p=94627#p94627

    Since I took the time to work on this and correct some (assumed) typos...
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  4. #4
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    Re: How to solve this function

    The Chaz, thanks for you help, I have just one question on the top:
    If they ask me to sketch f(x+0.5) is that mean that
    for
    f(x)=0 f(0+0.5) so: y=0.5 within (x<-1)
    f(x)=x+1 f(x+1+0.5) so y=x+1.5 within (-1<x<0)
    ...
    and so on?
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