The translation of the mapping \(T'U'V'W'\) onto \(TUVW\) is \(\boxed{(x,y)\rightarrow(x-3,y+3)}\).
Further explanation:
A transformation \(T:X\rightarrow Y\) is onto if any element of \(Y\) gives some element in \(X\) as the pre image of the translation in \(Y\).
Given:
The given translation \((x,y)\rightarrow(x+3,y-3)\)maps \(TUVW\) onto \(T'U'V'W'\).
Calculation:
The mapping \(T'U'V'W'\) onto \(TUVW\) is the backward translation of the mapping \(TUVW\) onto \(T'U'V'W'\).
In the given translation \((x,y)\rightarrow (x+3,y-3)\) the coordinates of the \(x\)-axis move by \(3\) units in the right direction and the coordinates of the \(y\)-axis move by \(3\) units in the downward direction.
So, for the mapping \(T'U'V'W'\) onto \(TUVW\) we have to move back to the original position.
The following steps are involved to reverse the mapping.
1) As earlier discussed the all \(x\)-coordinate move by \(3\) units in the right direction so the opposite of this is move all \(x\)-coordinate by \(3\) units in the left direction. Therefore, the translation for the \(x\)-axis would be \(x-3\).
2) As earlier the all \(y\)-coordinate move by \(3\) units in the downward direction so the opposite of this is move all \(y\)-coordinate by \(3\) units in the upward direction. Therefore, the translation for the \(x\)-axis would be \(y+3\).
Thus, the translation of the mapping \(T'U'V'W'\) onto \(TUVW\) is \(\boxed{(x,y)\rightarrow (x-3,y+3)}\).
Learn more:
1. A problem on inverse function https://brainly.com/question/1632445
2. A problem on domain and the range of the function https://brainly.com/question/3412497
3. A problem on range of the function https://brainly.com/question/1435353
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Function
Keywords: Onto mapping, one-one mapping, function, translation, x coordinate, y coordinate, coordinate, element, range , preimage, range, codomain, element, left direction, right direction, downward direction.
