To find the translation functions for the given points, we first identify the translations from each original point to its corresponding transformed point. Each original point (A, B, C) is translated by a certain horizontal shift \(h\) and a vertical shift \(k\) to reach their new positions (A’, B’, C’).
For point A (1, -1) to A’ (-7, -1), the \(x\)-coordinate changes from 1 to -7, resulting in a translation of \(h = -8\). The \(y\)-coordinate remains the same, indicating \(k = 0\).
For point B (5, -2) to B’ (-1, -4), the \(x\)-coordinate shifts from 5 to -1, resulting in \(h = -6\), and the \(y\)-coordinate changes from -2 to -4, giving \(k = -2\).
For point C (2, 3) to C’ (0, -3), the translation is \(h = -2\) for the \(x\)-coordinate and \(k = -6\) for the \(y\)-coordinate. Thus, the translation functions can be expressed as \(f(x) = x - 2\) and \(g(y) = y - 6\).
However, note that since each point has different shifts, there is no single pair of constant translations (h, k) that applies uniformly to all points, suggesting variable translations \(h\) and \(k\) for each pair.