To translate a point \((x, y)\) by 3 units to the right and 2 units down, we need to adjust the coordinates accordingly.
1. Translation to the right: When translating a point to the right, we add the number of units to the x-coordinate. Therefore, translating 3 units to the right from \((x, y)\) shifts the x-coordinate from \(x\) to \(x + 3\).
2. Translation downward: When translating a point downward, we subtract the number of units from the y-coordinate. Translating 2 units down from \((x, y)\) shifts the y-coordinate from \(y\) to \(y - 2\).
Putting these two translations together, the new coordinates of the point \((x, y)\) after being translated 3 units to the right and 2 units down are:
[tex]\[
(x + 3, y - 2)
\][/tex]
Thus, the function representing this translation is given by:
[tex]\[
f(x, y) = (x + 3, y - 2)
\][/tex]
To summarize, any point [tex]\((x, y)\)[/tex] will be translated to the point [tex]\((x + 3, y - 2)\)[/tex] when moved 3 units to the right and 2 units down.
