In each case, write the coordinate rule of the composition using the transformations F(x,y)=(2x,y) and G(x,y)=(x+3,-y)
1) G o F
2) F o G
3) G o G
4) F o F
And can you please tell me how you got your answers? Thanks!
1) G o F
2) F o G
3) G o G
4) F o F
And can you please tell me how you got your answers? Thanks!
-
Only for the first one:
GoF = G(F(x,y)) = G(2x, y) - here we substituted F(x, y) with (2x, y).
(x,y) = (x+3, -y). That is given a pair(x, y) you substitute it with (x+3, -y).
Now G(2x, y) = ((2x) + 3, -(y)) = (2x + 3, -y). So GoF(x,y) = (2x + 3, -y).
GoF = G(F(x,y)) = G(2x, y) - here we substituted F(x, y) with (2x, y).
(x,y) = (x+3, -y). That is given a pair(x, y) you substitute it with (x+3, -y).
Now G(2x, y) = ((2x) + 3, -(y)) = (2x + 3, -y). So GoF(x,y) = (2x + 3, -y).