To determine the values of \( h \) and \( k \) in the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to analyze the translation from point A (2, 2) to point A' (1, -3).
The translation affects the \( x \)-coordinate and the \( y \)-coordinate separately:
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For the \( x \)-coordinate comparison: \[ A = (2, 2) \quad \text{and} \quad A' = (1, -3) \] Using the function \( f(x) \): \[ f(2) = 2 + h = 1 \] To find \( h \), we solve: \[ 2 + h = 1 \implies h = 1 - 2 = -1 \]
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For the \( y \)-coordinate comparison: Using the function \( g(y) \): \[ g(2) = 2 + k = -3 \] To find \( k \), we solve: \[ 2 + k = -3 \implies k = -3 - 2 = -5 \]
Thus, the values are:
- The value of \( h \) is \( -1 \).
- The value of \( k \) is \( -5 \).
Final answer: The value of \( h \) is \(-1\) and the value of \( k \) is \(-5\).