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Thread: absolute value graphs

  1. #1
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    absolute value graphs

    Figure 1 shows the graph of y = f (x),
    The graph consists of two line segments that meet at the point P.
    The graph cuts the y-axis at the point Q and the x-axis at the points (3, 0) and R.

    given that $\displaystyle f(x) = 2 - |x+1 | $

    A) find the coordinates of P , Q and R.

    B) solve $\displaystyle f(x) = \frac{1}{2}x $
    I have found the coordinates of Q (0,1) , by putting x=0 and solving f(x).

    But I am not sure how to find R and P.

    Also for part 'B',
    should it be like this;

    $\displaystyle 2 - |x+1 |= \frac{1}{2}x $

    $\displaystyle 2 - |x+1 |= -\frac{1}{2}x $
    Attached Thumbnails Attached Thumbnails absolute value graphs-untitled.jpg  
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  2. #2
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    Quote Originally Posted by Tweety View Post
    I have found the coordinates of Q (0,1) , by putting x=0 and solving f(x).

    But I am not sure how to find R and P.

    Also for part 'B',
    should it be like this;

    $\displaystyle 2 - |x+1 |= \frac{1}{2}x $

    $\displaystyle 2 - |x+1 |= -\frac{1}{2}x $
    Use the definition of the absolute value:

    $\displaystyle |x+1|=\left\{\begin{array}{l}x+1,\ if \ x+1\ge 0~\implies~x\ge-1\\ -(x+1),\ if \ x+1< 0~\implies~x<-1 \end{array}\right.$

    The equation of the function becomes:

    $\displaystyle f(x)=\left\{\begin{array}{l}-x+1, \ x\ge-1\\x+3,\ x<-1\end{array}\right.$

    I'll leave the rest for you.
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