If a function is translated 6 units down, in which direction will the inverse of the functic be transformed? (1 point) The inverse of the given function will be translated 6 units down. The inverse of the given function will be translated 6 units left. The inverse of the given function will be translated 6 units up. The inverse of the given function will be translated 6 units right.

To determine how the inverse of a function is transformed when the original function is translated, we need to understand the relationship between a function and its inverse. 1. **Translation of the Function**: When a function \( f(x) \) is translated 6 units down, the new function can be expressed as: \[ g(x) = f(x) - 6 \] 2. **Finding the Inverse**: The inverse of a function \( f \) is denoted as \( f^{-1} \). The transformation of the inverse function is related to the transformation of the original function. 3. **Effect on the Inverse**: If the original function \( f(x) \) is translated down by 6 units, the inverse function \( f^{-1}(x) \) will be affected in the opposite direction. This is because the inverse function reflects the original function across the line \( y = x \). 4. **Conclusion**: Therefore, if the original function is translated 6 units down, the inverse function will be translated 6 units up. Thus, the correct answer is: **The inverse of the given function will be translated 6 units up.**