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

1. ## 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.

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

3. 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?