The translation functions for the given points can be defined by analyzing how each point shifts. For points A, B, and C, transforming them to their respective points A', B', and C' involves a horizontal shift of \(h\) and a vertical shift of \(k\). For point A, moving from (1, -1) to (-7, -1) indicates a horizontal translation of \(h = -8\) (1 to -7) and no vertical shift (\(k = 0\)). For points B and C, the translation can be determined as follows: B moves from (5, -2) to (-1, -4), which again gives \(h = -6\) and \(k = -2\). Lastly, point C moves from (2, 3) to (0, -3), indicating that \(h = -2\) and \(k = -6\). Therefore, we can summarize that the translation functions for points A, B, and C can be collectively expressed as \(f(x) = x - 8\) and \(g(y) = y - 6\).
Write the translation functions for the translation depicted below
f(x) = x+h
g(y)=y+k
Points are:
A (1,-1)
B (5,-2)
C (2,3)
A’ (-7,-1)
B’ ( -1,-4)
C’ (0,-3)
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