Question

find the image of the set s under the given transformation. the set s is the square bounded by the lines u = 0, u = 1, v = 0, and v = 1. the transformation is given by x = v, y = u(1 v 2 ).

Answer 1

To find the image of the square set S under the given transformation equations x=v and y=u(1+v^2), we transform each vertex of the square to obtain the vertices of the image as a skewed quadrilateral in the x-y plane.

Step-by-step explanation:

To find the image of the set S under the given transformation with the square bounded by the lines u = 0, u = 1, v = 0, and v = 1, we will apply the given transformation equations x = v and y = u(1 + v2). We perform this transformation for each vertex of the square:

1. For the vertex at (u, v) = (0, 0), the image is (x, y) = (0, 0).
2. For the vertex at (u, v) = (1, 0), the image is (x, y) = (0, 1).
3. For the vertex at (u, v) = (0, 1), the image is (x, y) = (1, 0).
4. For the vertex at (u, v) = (1, 1), the image is (x, y) = (1, 2).

By connecting these transformed points, we can visualize the new image of the set S as a skewed quadrilateral in the x-y plane.