Chapter 5.7, Problem 360E

In the following exercises, the function

$T:S\to R,T\left(u,v\right)=\left(x,y\right)$ on the region

$S=\left\{\left(u,v\right)|0\le u\le 1,0\le v\le 1\right\}$ bounded by the unit square is given, where $R\subset R^2$ is the image of S under

a. Justify that the function T is a C transformation.

b. Find the images of the vertices of the unit square S through the function T.

c. Determine the image R of the unit square S and graph it.

360. $x=u^3,u=v^2$