anonymous
  • anonymous
Find the image of the set S under the given transformation: u=0, u=1, v=0, v=1, x=v, y=u(1+v^2)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
plug in \(x(0,0), x(1,1), y(0,0), y(1,1)\)
anonymous
  • anonymous
Yes, that's the function. That's it?
anonymous
  • anonymous
No, that's the function. The image is the range of values you get from the "domain" S.

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anonymous
  • anonymous
Seems to me that \[ x(0,0) \leq x \leq x(1,1) \]
anonymous
  • anonymous
Alright, I have (0,0)->(0,0) (1,0)->(1,1) (0,1)->(0,0) (1,1)->(1,2) Is that it?
anonymous
  • anonymous
Look at the highest and lowest of x and y.
anonymous
  • anonymous
@Wislar are you implying that \(S = \{0, 1\} \times \{0, 1\}\)? From your question, it seems to just be \(S = \{ (0,0), (1,1)\}\). Please clarify.
anonymous
  • anonymous
The points on the first image are (0,0), (1,0), (1,1), (0,1) which is a square and plugging those into the equations for x=v and y=u(1+v^2) to get those points
anonymous
  • anonymous
Then your image is the set of all the transformed points.
anonymous
  • anonymous
So I had to correctly?
anonymous
  • anonymous
it**
anonymous
  • anonymous
Well, I'm not going to check your arithmetic, but it should be the four points on the right side of your arrows in your above comment. Also make sure that \(S\) only relates to those four points, and is NOT defined by \(S = \{(u, v) | u \in [0,1] \land v \in [0,1]\}\)
anonymous
  • anonymous
That's what I did. Thanks!

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