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Homework Help: Draw a contour map of the function showing several level curves.

  1. Nov 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Draw a contour map of the function showing several level curves.

    f(x,y) = x^3 - y


    2. Relevant equations

    f(x, y) = x^3 - y

    3. The attempt at a solution
    I think I should be finding the domain and range, but other than that I am not sure what else I need to do.
     
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  3. Nov 1, 2008 #2

    HallsofIvy

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    ??? You need to do what you are told to do: Draw several curves of the contour map! That has nothing to do with finding "domain" and range".
    Graph x^3- y= -1.
    Graph x^3- y= 0.
    Graph x^3- y= 1.
    Graph x^3- y= 2. etc.
     
  4. Nov 1, 2008 #3

    Office_Shredder

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    A level curve is when f(x,y) is constant. So you're looking at [tex]x^3 - y = c[/tex] for some c a real number. Try starting with c=0, then see how to modify the level curve when c changes
     
  5. Nov 1, 2008 #4
    Okay, I understand what you mean by making it equal that constant and then set the constant to a number of different values, but I'm having a difficult time putting the equation into a way that I can quasi-graph it.
     
  6. Nov 1, 2008 #5

    HallsofIvy

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    Why "quasi-graph" it? Why not just graph them:

    y= x3+ 1,
    y= x3,
    y= x3- 1,
    y= x3- 2, etc.
    can't be all that hard to graph!
     
  7. Nov 1, 2008 #6

    Office_Shredder

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    You should be able to graph y = x3 in the plane at the very least
     
  8. Nov 1, 2008 #7
    oh yeah, sorry that I didn't reply earlier. I graphed them with no problem. what I meant by 'quasi-graph' is that it is a contour graph, not the usual kind.
     
  9. Nov 2, 2008 #8

    HallsofIvy

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    What do you see as a difference between a "contour map" and "the usual kind"?
     
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