A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes as shown in the figure below. (Enter your answers as a comma-separated list of equations.)
R is bounded by y = 2x − 2, y = 2x + 2, y = 2 − x, y = 4 − x

Question

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v-axes as shown in the figure below. (Enter your answers as a comma-separated list of equations.)
R is bounded by y = 2x − 2, y = 2x + 2, y = 2 − x, y = 4 − x

anonymous · Answer

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anonymous · Answer

I'm not even sure where to begin with the relation of the two.

I can't say when x is this u is this because the equations only have variables x and y.

The only relation is the graph but I'm not sure how I can when uv is (0,4) xy is (x,y)

anonymous · Answer

@Concentrationalizing @sidsiddhartha

anonymous · Answer

Figured it out, an explanation can be given if curious.

anonymous · Answer

@114Bytes 
I didnt get the time today to try and respond to this question. Usually they don't make you figure out the region, they give you some sort of transformation to use, x = u + v, y = v/2, etc. 

If I had to guess, I would say you would have needed to set up the integral as if you weren't going to transform it, and then pick your u and v subs based on what integral you got. I could be wrong, though, lol.

anonymous · Answer

That's all right all that was needed for was find some function of x and y set it equal to u and do the same for v

anonymous · Answer

I wouldve thought the transformation would have to be a lot pickier than that but if it worked, then awesome, lol.