Thread: 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.

Hello, Zedd!

Provide a function that has this graph:

Code:

              |
      *       |               *
          *   |           *
             *|        *
              |*     *
              | *   *
              |  * *
              |
              |   *
              |
    - - - - - + - - - - - - - - -
              |

One function that has a "cusp" is: .$\displaystyle 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: .$\displaystyle y \:=\:(x-1)^{\frac{2}{3}} + 1$

Originally Posted by Soroban

Hello, Zedd!


One function that has a "cusp" is: .$\displaystyle 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: .$\displaystyle y \:=\x-1)^{\frac{2}{3}} + 1$

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?