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Math Help - What is the function for a graph that looks like this?

  1. #1
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    What is the function for a graph that looks like this?

    http://upload.wikimedia.org/wikipedi...x_function.png

    I'm doing my Economics math homework, and we were asked to provide a function that is quasiconvex, but not convex. This graph is both of those things; however, I don't know what the function would be. Any help would be appreciated.
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  2. #2
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    Hello, Zedd!

    Provide a function that has this graph:
    Code:
                  |
          *       |               *
              *   |           *
                 *|        *
                  |*     *
                  | *   *
                  |  * *
                  |
                  |   *
                  |
        - - - - - + - - - - - - - - -
                  |

    One function that has a "cusp" is: . y \:=\:x^{\frac{2}{3}} , which has its cusp at the origin.
    . . [It is called a "semicubical parabola."]

    Your function has its cusp moved to (1,1), perhaps.

    Its equation is: . y \:=\:(x-1)^{\frac{2}{3}} + 1

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, Zedd!


    One function that has a "cusp" is: . y \:=\:x^{\frac{2}{3}} , which has its cusp at the origin.
    . . [It is called a "semicubical parabola."]

    Your function has its cusp moved to (1,1), perhaps.

    Its equation is: . x-1)^{\frac{2}{3}} + 1" alt="y \:=\x-1)^{\frac{2}{3}} + 1" />

    Thank you so much! Are you familiar at all with quasiconvexity? What makes this function quasiconvex? My notes say that its because the worse set is convex... is that correct?
    Last edited by Zedd; March 1st 2009 at 08:35 PM.
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