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From Mathematics: General-Mathematics
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Due on Mar. 04, 2009
Asked on Mar 03, 2009 at 7:37:00PM

Q:
Let S be the subset of R^2 defined by

S={(x,y) in R^2:x<4, y>0, 2y<x-2}

and let f and g be the function defined by
f:R^2 ----> R^2
(x,y) |----> (x+1,y-2)
and
g:R^2 ---> R^2
(x,y) |----> (y,-x)

a) Describe the geometric effect on each of f and g.
b) Any idea how i can sketch the set S and and its image under each of the functions f and g. (any points i can plot would help)
c) Determine the composite function g o f (and what the sketck of the image of S under g o f would be)

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alephzero314
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$2.00 Full Solution with picture of S

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Posted on Mar 03, 2009 at 8:10:45PM

A:
Preview: ... n. It moves a point horizontally 1 unit to the right and 2 units down. g is a clockwise rotation by 90 degrees. (Try inputting some points to see this). b) Sketching the set S: I've included a sketch of the end result. The set is the filled in triangle. The lines on the graph are not included in the set S, but they help find it's boundary, so I left them in the picture. You have to include all points in the plane that satisfy all three conditions. To find all point ...

The full tutorial is about 415 words long plus attachments.

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TheSetS.JPG (121K) (Preview)