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

• Mar 1st 2009, 07:51 PM
Zedd
What is the function for a graph that looks like this?

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.
• Mar 1st 2009, 08:54 PM
Soroban
Hello, Zedd!

Quote:

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

• Mar 1st 2009, 09:21 PM
Zedd
Quote:

Originally Posted by Soroban
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: . $y \:=\:(x-1)^{\frac{2}{3}} + 1$

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?