To determine the values of \( h \) and \( k \) in the functions \( f(x) = x + h \) and \( g(y) = y + k \), we need to know the specific translation that was applied to triangle \( ABC \) to obtain triangle \( A'B'C' \).
In general, if the triangle is translated horizontally \( h \) units and vertically \( k \) units, then:
- \( h \) represents the horizontal shift. If the triangle moves to the right, \( h \) is positive. If it moves to the left, \( h \) is negative.
- \( k \) represents the vertical shift. If the triangle moves upwards, \( k \) is positive. If it moves downwards, \( k \) is negative.
To find the exact values, you would normally observe the coordinates of a point before and after the translation:
- If point \( A(x_1, y_1) \) moves to point \( A'(x_2, y_2) \), then:
- \( h = x_2 - x_1 \)
- \( k = y_2 - y_1 \)
Without the specific coordinates provided in the image you're referencing, we cannot calculate the exact numerical values for \( h \) and \( k \). Please provide the coordinates of the triangles or describe the translation, and I can help determine the values.