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Homework Help: Sketch the curves y =|x| and y = 2 - x^2 on the graphs

  1. Jun 21, 2007 #1
    1. The problem statement, all variables and given/known data
    Sketch on the same axis the graphs of y = |x| and y = 2 - x^2.

    For which values f x is the inequality |x| < 2 - x^2


    2. Relevant equations



    3. The attempt at a solution

    I don't really understand what it is asking me to do, i've sketched the two curves, y = |x| 45 degrees from the x axis and at -45 degrees from the x axis, and the curve y = 2 - x^2 is an upside down quadratic curve with the vertex at -2 y.

    thanks
     
  2. jcsd
  3. Jun 21, 2007 #2

    malawi_glenn

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    for which values of x is the graph of y = |x| under the graph of y = 2 - x^2 ?
     
  4. Jun 21, 2007 #3
    is that what its asking?

    if so how do i work that out, is it similar to the wa you work out whether a curve crosses the x-axis.

    thanks
     
  5. Jun 21, 2007 #4

    malawi_glenn

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    you first draw graphs, then find the points of intersection for the relevant places.
     
  6. Jun 21, 2007 #5
    ok, but how?? :S
     
  7. Jun 21, 2007 #6

    malawi_glenn

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    if you have drawn the graphs you jsut plug in |x| in the y = 2 - x^2

    so we get:

    x = 2 - x^2, for x > 0

    and

    -x = 2 - x^2, for x < 0

    points of intersection is where the two graphs/functions are equal...
     
    Last edited: Jun 21, 2007
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