Respuesta :
Given:
The pre-image coordinates (0, 5), (-3, 2), (4, -1) and transformed image coordinates (2, -5), (-1, -2), (6, 1).
Required:
We need to find the transformation in function notation.
Explanation:
Let (x,y) be the pre-image coordinate and (x',y') be the transformed image coordinates.
The transformation is
[tex](x,y)\rightarrow(x^{\prime},y^{\prime}).[/tex]Consider the points (0,5) and (2,-5).
Substitute the values in the transformation.
[tex](0,5)\rightarrow(2,-5)[/tex][tex](0,5)\rightarrow(0+2,-(5))[/tex]Let x =0 and y =5, we get
[tex](x,y)\rightarrow(x+2,-y)[/tex]Consider the points (-3,2) and (-1,-2).
[tex](-3,2)\rightarrow(-1,-2)[/tex][tex]Use\text{ }-3+2=-1.[/tex][tex](-3,2)\rightarrow(-3+2,-(2))[/tex]Let x =-3 and y=2.
[tex](x,y)\rightarrow(x+2,-y)[/tex]Consider the points (4,-1) and (6,-1).
[tex](4,-1)\rightarrow(6,1)[/tex][tex]Use\text{ }4+2=6.[/tex][tex](4,-1)\rightarrow(4+1,-(1))[/tex][tex](x,y)\rightarrow(x+2,-y)[/tex][tex]f(x,y)=(x+2,-y)[/tex]Final answer:
[tex](x,y)\rightarrow(x+2,-y)[/tex][tex]f:(x,y)\rightarrow(x+2,-y)[/tex]