If a function is translated 9 units to the left, in which direction will the inverse of the function be transformed? (1 point) The inverse of the given function will be translated 9 units down. The inverse of the given function will be translated 9 units up. The inverse of the given function will be translated 9 units to the left. The inverse of the given function will be translated 9 units to the 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 9 units to the left, the new function can be expressed as \( f(x + 9) \). 2. **Finding the Inverse**: The inverse function \( f^{-1}(y) \) essentially swaps the roles of \( x \) and \( y \). If we have \( y = f(x) \), then the inverse is defined by \( x = f^{-1}(y) \). 3. **Effect on the Inverse**: If the original function \( f(x) \) is translated to \( f(x + 9) \), we can express the inverse of the translated function. The new function can be represented as: \[ y = f(x + 9) \] To find the inverse, we swap \( x \) and \( y \): \[ x = f(y + 9) \] Solving for \( y \) gives us the inverse of the translated function. 4. **Conclusion**: The transformation indicates that the inverse function will be translated 9 units to the right. Thus, the correct answer is: **The inverse of the given function will be translated 9 units to the right.**