To determine the values of \( h \) and \( k \) for the translation functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to understand how the translation works.
When triangle ABC is translated to produce triangle A' B' C", the coordinates of each vertex of triangle ABC change. If vertex A has coordinates \( (x_A, y_A) \) and it translates to vertex A' with coordinates \( (x_{A'}, y_{A'}) \), then the translation can be described as:
- \( x_{A'} = x_A + h \)
- \( y_{A'} = y_A + k \)
From this, we can express \( h \) and \( k \) as follows:
- \( h = x_{A'} - x_A \)
- \( k = y_{A'} - y_A \)
Thus, \( h \) is the change in the x-coordinate and \( k \) is the change in the y-coordinate as triangle ABC is moved to triangle A' B' C".
To find the specific numerical values of \( h \) and \( k \), you would need the original coordinates of triangle ABC and the new coordinates of triangle A' B' C".