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Math Help - Piece wise function graphs

  1. #1
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    Piece wise function graphs

    Is my graph correct? How do I find the range according to the graph?
    let f(x) = |x+4|-1, -6 \leq x<-3
    9-x^2, -2< x \leq 1
    (/sqrtx-2)+2, 2 \leq x < 6
    Attached Thumbnails Attached Thumbnails Piece wise function graphs-graph.jpg  
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  2. #2
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    Quote Originally Posted by dorkymichelle View Post
    Is my graph correct? How do I find the range according to the graph?
    let f(x) = |x+4|-1, -6 \leq x<-3
    9-x^2, -2< x \leq 1
    (/sqrtx-2)+2, 2 \leq x < 6
    Hi dorkymichelle,

    Well, I don't get what you got. I don't have a graphing program where I can show you, but here are the three functions and tables. Graph them and see the differences.


    <br />
f(x)=\begin{cases}[1] \ \ |x+4|-1, & \text{ if }-6 \leq x <-3 \\ [2] \ \ 9-x^2, & \text{ if }x \leq 1 \\ [3] \ \ \sqrt{x-2}+2, & \text{ if } 2\leq x < 6 \end{cases}

    Branch [1]: f(x)=|x+4|-1 \ \ if \ \ -6 \leq x < -3
    Code:
    x | f(x)
    --|-----
    -6| 1  Closed
    -5| 0
    -4| -1
    -3| 0  Open
    Branch [2]: f(x)=9-x^2 \ \ if \ \ x \leq 1

    Code:
    x | f(x)
    --|-----
    1 | 8  Closed
    0 | 9  
    -1| 8
    -2| 5
    -3| 0 No reason to stop here!
    -4| -7
    Branch [3]: f(x)=\sqrt{x-2}+2 \ \ if \ \ 2 \leq x<6

    Code:
    x | f(x)
    --|-----
    2 | 2  Closed
    3 | 3
    6 | 4  Open
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