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Math Help - Piecewise functions

  1. #1
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    Piecewise functions

    How would I graph that, what would it look like?

    x-2 : -8X0
    2^x : -8<x<0
    -2(x-4) : 2X8
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  2. #2
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    a good strategy:

    Quote Originally Posted by olen12 View Post
    How would I graph that, what would it look like?

    x-2 : -8X0
    2^x : -8<x<0
    -2(x-4) : 2X8

    First, you obviously need the graph paper or sheet. Something with a grid.
    Establish your x and y axes.
    The first thing you need to do is solve for y=x-2 at -8. Then do the same at -2. I would hope that you know that x-2 is a straight line, so plug in those two coordinates on your grid and connect them. since the signs are not OR EQUAL TO (meaning that the bounds are -8<x<0, not -8≤x≤0), you need to have open circles, like this at either end of your line, like this: o

    Next, you find y=2^x for x=-8 and x=0. Plug in those two coordinates. Since this is a power function, it will be a curve. What you should do to find out how that curve fits is find y=2^x for points in the middle, such as -6, -4, and -2, then fit the best line you can. Since these signs ARE EQUAL TO ( -8≤x≤0), you need closed circles at either end, like this: .

    The last function you do the same. Plug in both ends and put open circles there. since this graph is linear, just draw a straight line between them.
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  3. #3
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    I'm a bit confused, say for this conditional: -8X0
    Does that mean do x-2 while -8 is less then x and x is less then 0?
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  4. #4
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    bump
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  5. #5
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    Draw vertical lines in light pencil (since they won't be part of the graph) at x= -8, 0, 2, and 8.

    Draw the graph of y= x- 2 (a straight line, of course) also in light pencil and erase any part of it that is to the right of the line x= -8. Draw the rest, to the left of x= -8, in dark pencil or ink.

    Draw the graph of y= 2^x in light pencil. Erase that part that is to the left of x= -8 or to the right of x= 0. Draw the rest, between x=-8 and x=0, in dark pencil or pen. Also, because this section includes "-8= x" and "x= 0", mark dark "dots" at the ends of that graph.

    Draw the graph of y= -2(x- 4) (again a line). Erase that part that is to the left of x= 2 and to the right of x= 8. Draw the part between x= 2 and x= 8 in dark pencil or ink. Notice that there is no graph between x= 0 and x= 2. That is because your function is not defined there.
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  6. #6
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    Is this correct by any chance? I tried to use winplot to graph it.
    Attached Thumbnails Attached Thumbnails Piecewise functions-g.jpg  
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