Question

Given the range (1, 1), (4, 2), (2, -1), with a coordinate transformation of f(x, y) = (x+2, y-3), what is the domain?

Answer 1

Given:

$Range:(1,1),(4,2),(2,-1)$

To Determine: The domain if the coordinate of transformation is f(x, y) = (x + 2, y - 3)

Solution

$\begin{gathered} f(x,y)=(x+2,y-3) \\ Therefore \\ (1,1)\rightarrow(1+2,1-3) \\ (1,1)\rightarrow(3,-2) \end{gathered}$$\begin{gathered} (4,2)\rightarrow(4+2,2-3) \\ (4,2)\rightarrow(6,-1) \end{gathered}$$\begin{gathered} (2,-1)\rightarrow(2+2,-1-3) \\ (2,-1)\rightarrow(4,-4) \end{gathered}$

Therefore

$(1,1),(4,2),(2,-1)\rightarrow(3,-2),(6,-1),(4,-4)$

Hence, the domain is 3, 6, 4 as shown in (3, -2), (6, -1), (4, -4)