To determine the correct function rule for translating a square on a coordinate plane, we need to consider how translation affects the coordinates of any point \((x, y)\) on the square.
1. Translating Down:
- Translating a figure 9 units down affects the \(y\)-coordinate. To move a point down, we subtract 9 from the \(y\)-coordinate. Therefore, the \(y\)-coordinate of a point \((x, y)\) will become \(y - 9\).
2. Translating to the Right:
- Translating a figure 1 unit to the right affects the \(x\)-coordinate. To move a point to the right, we add 1 to the \(x\)-coordinate. Therefore, the \(x\)-coordinate of a point \((x, y)\) will become \(x + 1\).
Combining these translations, the new coordinates for any point \((x, y)\) after translating 9 units down and 1 unit to the right will be:
[tex]\[
(x + 1, y - 9)
\][/tex]
We denote this function rule using transformation notation \(T_{a, b}(x, y)\), where \(a\) is the change in the \(x\)-coordinate and \(b\) is the change in the \(y\)-coordinate. Here, \(a = 1\) and \(b = -9\).
Thus, the translation function is:
[tex]\[
T_{1, -9}(x, y)
\][/tex]
Therefore, the correct function rule that describes the translation is:
[tex]\[ T_{1, -9}(x, y) \][/tex]
