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Sagot :
Answer:
1) [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
Coordinate change
(x, y) → (x + a, y + b)
2) RFy(x, y) = f(-x)
Coordinate change
(x, y) → (-x, y)
3) RFx(x, y) = -f(x)
Coordinate change
(x, y) → (-y, x)
4) RCCW90(x, y) = f⁻¹(-x)
Coordinate change
(x, y) → (-y, x)
5) RCCW180(x, y) = -(f(-x))
Coordinate change
(x, y) → (-x, -y)
6) A 270 degrees counterclockwise rotation gives;
RCCW270(x, y) = -(f⁻¹(x))
Coordinate change
(x, y) → (y, -x)
Step-by-step explanation:
1) Horizontal translation a units right = f(x - a)
The vertical translation b units up = f(x) + b
Therefore, we get; [tex]T_{(a, \, b)}[/tex] = f(x - a) + b
The coordinate change
(x, y) → (x + a, y + b)
2) A reflection across the y-axis = RFy(x, y) = f(-x)
The coordinate change
(x, y) → (-x, y)
3) A reflection across the x-axis gives RFx(x, y) → (x, -y)
Therefore, in function notation, we get;
RFx(x, y) = -f(x)
4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)
In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)
5) A 180 degrees counterclockwise rotation about the origin gives;
(x, y) → (-x, -y)
Therefore, we get;
In function notation RotCCW180(x, y) = -(f(-x))
6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)
In function notation RotCCW270(x, y) = -(f⁻¹(x))
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